a new mixed finite element for the stokes and elasticity problems the stokes problem is approximated by a mixed finite element method using a new finite el ement which has properties analogous to the finite volume methods namely the local conservation of the momentum and the mass estimates of optimal order are derived for the errors in the velocity the pressure and the gradient of the velocity this new finite element also works for the elasticity problem and all estimates are valid uniformly with respect to the compressibility finally some numerical results for the incompressible navier stokes equations are presented

a coupled finite volume solver for the solution of incompressible flows on unstructured grids this paper reports on a newly developed fully coupled pressure based algorithm for the solution of laminar incompressible flow problems on collocated unstructured grids the implicit pressure velocity coupling is accomplished by deriving a pressure equation in a procedure similar to a segregated simple algorithm using the rhie chow interpolation technique and assembling the coefficients of the momentum and continuity equations into one diagonally dominant matrix the extended systems of continuity and momentum equations are solved simultaneously and their convergence is accelerated by using an algebraic multigrid solver the performance of the coupled approach as compared to the segregated approach exemplified by simple is tested by solving five laminar flow problems using both methodologies and comparing their computational costs results indicate that the number of iterations needed by the coupled solver for the solution to converge to a desired level on both structured and unstructured meshes is grid independent for relatively coarse meshes the cpu time required by the coupled solver on structured grid is lower than the cpu time required on unstructured grid on dense meshes however this is no longer true for low and moderate values of the grid aspect ratio the number of iterations required by the coupled solver remains unchanged while the computational cost slightly increases for structured and unstructured grid systems the required number of iterations is almost independent of the grid size at any value of the grid expansion ratio recorded cpu time values show that the coupled approach substantially reduces the computational cost as compared to the segregated approach with the reduction rate increasing as the grid size increases

periodic solutions of a class of dynamical systems of second order abstract we give some sufficient conditions for the existence of infinitely many periodic solutions with prescribed period for a class of dynamical systems of second order variational methods and finite dimensional approximations are used

a symplectic fixed point theorem for cpn two symplectic diffeomorphisms 0 1 of a symplectic manifold x are said to be homologous if there exists a smooth homotopy 1 t 0 1 of symplectic diffeomorphisms between them such that the timedependent vector field t defined byd dt t t o t is a globally hamiltonian vector field for allt i e there exists a smooth real valued timedependent hamiltonian functionh x t onx x 0 1 such that t dh t whereht h x t

solution of the implicitly discretised reacting flow equations by operator splitting abstract a non iterative method for handling the coupling of the implicitly discretised time dependent fluid flow equations is described the method is based on the use of pressure and velocity as dependent variables and is hence applicable to both the compressible and incompressible versions of the transport equations the main feature of the technique is the splitting of the solution process into a series of steps whereby operations on pressure are decoupled from those on velocity at each step with the split sets of equations being amenable to solution by standard techniques at each time step the procedure yields solutions which approximate the exact solution of the difference equations the accuracy of this splitting procedure is assessed for a linearised form of the discretised equations and the analysis indicates that the solution yielded by it differs from the exact solution of the difference equations by terms proportional to the powers of the time step size by virtue of this it is possible to dispense with iteration thus resulting in an efficient implicit scheme while retaining simplicity of implementation relative to contemporary block simultaneous methods this is verified in a companion paper which presents results of computations carried out using the method

forced vibrations of superquadratic hamiltonian systems on etudie l existence des solutions t periodiques ter t 0 du systeme hamiltonien suivant z gh z f t ou g est la matrice asymetrique standard

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

application of time iterative schemes to incompressible flow the computation of steady incompressible flows by an euler implicit algorithm is studied using both the incompressible equations and the low mach number compressible equations the incompressible equations are handled by adding an artificial time derivative to the continuity equation this allows both the pressure and velocity to be obtained implicitly in one dimensional problems both systems converge rapidly even at low mach numbers where the eigenvalues are very stiff in two dimensions where approximate factorization is required the presence of stiff eigenvalues is highly detrimental stiffness can be avoided in the incompressible equations by selecting an appropriate pseudo mach number this insures reliable convergence and results in an efficient incompressible flow algorithm in the case of compressible equations the mach number cannot be chosen arbitrarily and the contamination introduced by approximate factorization must be removed a matrix preconditioning factor that accomplishes this is developed and demonstrated with this modification the convergence rate is the same as in the incompressible case and is independent of mach number rapid convergence is observed at mach numbers as low as 6 05

solutions of perturbed p laplacian equations with critical nonlinearity in this paper we study a perturbed p laplacian equation under some given conditions on v x we prove that the equation has at least one positive solution provided that e e for any n n it has at least n pairs solutions if e en and suppose there exists an orthogonal involution t rn rn such that v x p x and k x are t invariant then it has at least one pair of solutions which change sign exactly once provided that e e where e and en are sufficiently small positive numbers moreover these solutions ue 0 in w1 p rn as e 0

three dimensional grid generation using elliptic equations with direct grid distribution control boundary fitted computational meshes are generated by solving a system of elliptic partial differential equations the grid points at the boundary surfaces are arbitrarily distributed the interior grid distribution is controlled by a technique which insures a grid line orthogonality at the boundaries the grid is automatically adjusted while the grid line orthogonality at the boundaries is achieved in an iterative process this technique is demonstrated for three different configurations desirable cell size and shape are obtained for the boundary shapes which normally cause poor grid distribution

on the periodic fucik spectrum and a superlinear sturm liouville equation in the first part of the paper a variational characterisation of the periodic eigenvalues the so called fucik spectrum of a semilinear positive homogeneous sturm liouville equation is given the proof relies on the s 1 invariance of the equation in the second part a nonlinear sturm liouville equation with typically an exponential nonlinearity is considered it is proved that under certain conditions this equation is solvable for arbitrary forcing terms the proof uses a comparison of the minimax levels of the functional associated to this equation with suitable values in the fucik spectrum

on the dimension and the index of the solution set of nonlinear equations we study the covering dimension and the index of the solution set to multiparameter nonlinear and semilinear operator equations involving fredholm maps of positive index the classes of maps under consideration are pseudo a proper and either approximation essential or equivariant approximation essential applications are given to semilinear elliptic bvp s

multiplicity results of periodic solutions for a class of second order delay differential systems abstract this paper is concerned with the periodic boundary value problem 1 u t u t f t u t a e t 0 2 u 0 u 2 u 0 u 2 0 where 0 is a given constant r is a parameter the variational principle is given and some multiplicity results of periodic solutions of 1 are obtained directly via variational methods

equivariant morse theory for flows and an application to the n body problem a l aide de l indice de conley et de la cohomologie equivariante on deduit certaines inegalites de type morse pour un flot equivariant par rapport a l action d un groupe topologique compact

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

a simple and efficient segregated smoother for the discrete stokes equations we consider the multigrid solution of the generalized stokes equations with a segregated i e equationwise gauss seidel smoother based on a uzawa type iteration we analyze the smoother in the framework of local fourier analysis and obtain an analytic bound on the smoothing factor showing uniform performance for a family of stokes problems these results are confirmed by the numerical computation of the two grid convergence factor for different types of grids and discretizations numerical results also show that the actual convergence of the w cycle is approximately the same as that obtained by a vanka smoother despite this latter smoother being significantly more costly per iteration step

multiple solutions of hamiltonian systems via limit relative category by means of an extension of relative category we prove by a linking type theorem the existence of two distinct critical levels for a strongly indefinite functional applications to asymptotically linear hamiltonian systems are given

nonlinear problems with strong resonance at infinity an abstract theorem and applications on considere l equation au n u u e ou a est un operateur lineaire n avec c 1 e r et e est un espace de hilbert on suppose que n a une derivee a l infini n et que o appartient au spectre de a n on demontre un theoreme pour la multiplicite des solutions

periodic solutions of symmetric autonomous newtonian systems abstract in this paper we show the existence and bifurcation of t periodic solutions of a special form for an autonomous newtonian system with symmetry if the phase space r 2 n is equipped with the structure of an orthogonal representation w w and the potential v w r is invariant then for every such a solution the set of indices of nonvanishing fourier coefficients is finite and depends on w only if the potential v depends on the squares of complex coordinates then for every such a solution t is the minimal period

multiple critical points of invariant functionals and applications abstract this paper deals with some multiplicity results of periodic orbits of hamiltonian systems and for solution of a non linear dirichlet problem these results follow from an abstract theorem of lusternik schnirelman type as applied to an invariant equation of the form lu delta f u 0 in a hilbert space x l sub 2 omega r sub n where l is an unbounded self adjoint operator and f is a c sub 1 strictly convex function author

a numerical model for flow in meandering channels with natural bed topography a finite volume numerical model is presented for the calculation of three dimensional turbulent flow in meandering channels with natural bed configuration the governing equations are written in a general curvilinear coordinate system so that all singly connected geometrical configurations can be accommodated for simplicity the cartesian velocity components are retained as dependent variables the numerical procedure is very general so that it can deal with complex cross sections and separated flow turbulence closure is through the standard k model computed results show good agreement with experimental data in meandering channels with rectangular and natural bed configurations this work provides a hydrodynamic basis for the study of the mechanisms for the formation of river meanders

nontrivial periodic solutions for delay differential systems via morse theory abstract the existence of the nontrivial periodic solutions to the system of delay differential equations 1 1 x t f x t is investigated where x r n f c r n r n we prove several new existence results via morse theory and the galerkin methods

a borsuk ulam theorem for orthogonal tk and zpr actions and applications abstract a version if the borsuk ulam theorem is proved for the torus tk and p torus zpr we deal with the case of a nonempty fixed point set of groups on the sphere of representation as an application a geometrical index theory is introduced for these groups the index is used to obtain the existence of multiple critical points for functions invariant under tk or zpr action

periodic solutions of a class of singular hamiltonian systems soit r n 0 n n n 3 et soit v c 1 rx r on etudie l existence des solutions periodiques t u t avec une periode prescrite du systeme suivant de n equations differentielles d ordre 2 u v t u

infinitely many solutions of a symmetric dirichlet problem here q is a bounded domain in r with smooth boundary and f i r is c and satisfies certain growth conditions if m 1 and f is an even function hence f r r is an odd function then ambrosetti and rabinowitz l 21 proved the existence of infinitely many weak solutions of d using a symmetric version of the mountain pass theorem a similar result is due to michalek 3 who considered the case where m 21 rm s c and f is invariant under a free action of the cyclic group z p on c here z p is considered as a subgroup of s c c acting essentially via scalar multiplication on c in this paper we want to investigate which kind of symmetries guarantee the existence of infinitely many solutions of d let g be a compact lie group and p g o m an orthogonal representation of g on lrm then g acts on irm via the map g x ir ir g u y gv p g v we write v for the space rm considered as a g space do there exist infinitely many solutions of d if f is invariant under this symmetry i e f gu f u for all g e g and u e v without further assumptions on p the answer to this question is no in general for example if p g id for all g e g then there is no symmetry at all and one cannot expect infinitely many solutions more generally one should exclude the existence of fixed points vg u e vi gu u for all g e g 0 our first result says that there exist infinitely many solutions of d if the following condition is satisfied

lusternik schnirelman method for functionals invariant with respect to a finite group action has at least g i n 1 distinct critical points see kl ma we refer also to corollary 1 5 which is a generalization of this result consequently the existence of a symmetry group g for the func tionalf in general defined on a banach manifold has a significant impact on the number of critical points the problem of finding the best possible estimates for the number of orbits of critical points of an invariant func tional was studied by many authors for a i action with p prime number see el for s action see bl b2 cw2 cw3 fr2 r2 for a non free action where morse theory is applied see pl cwl w see also da fh frl this work is an attempt to give a general and explicit formula cf theorem 1 3 for the number of critical points of an invariant func tional

periodic solutions of dynamical systems with bounded potential where ve c2 r x rn r v t t x y t x v t x jjbxiw y is bounded and v v t x 0 as 1x1 co for example we prove that if 0 d v r x m and v r x m as 1x1 co there exists at least one t periodic solution of v moreover if v j t 0 0 under suitable assumptions on v y t 0 this solution is not identically zero we also give existence results for the forced system

semiclassical states for nonlinear schrodinger equations with sign changing potentials we establish the existence and multiplicity of semiclassical bound states of the following nonlinear schrodinger equation e2 u v x u g x u for x rn u x 0as x where v changes sign and g is superlinear with critical or supercritical growth as u

infinitely many periodic solutions for second order hamiltonian systems in this paper we study the existence of infinitely many periodic solutions for second order hamiltonian systems u uv t u 0 where v t u is either asymptotically quadratic or superquadratic as u

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

finite volume methods for two dimensional incompressible flows with complex boundaries abstract the paper discusses possible ways of developing accurate and efficient finite volume methods for complex incompressible flows the issues of boundary fitted grid generation choice of coupled or uncoupled procedures cartesian or grid aligned velocity components staggered or non staggered variable arrangement discretization methods solution algorithms and convergence acceleration by multigrid methods are addressed an example of a finite volume method for general two dimensional flows is described in some detail and applications of this method to a variety of flows are presented

homoclinic solutions of hamiltonian systems with symmetry abstract we prove the existence of infinitely many homoclinic solutions for a first order hamiltonian system symmetric with respect to an action of a compact lie group by means of variational methods we make no convexity assumption on the hamiltonian

kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow the collocated mesh scheme is often favored over the staggered mesh scheme for turbulence simulation in complex geometries due to its simpler form in curvilinear coordinates the collocated mesh scheme does not conserve kinetic energy however and few careful checks of the impact of these errors have been made in this work analysis is used to identify two sources of kinetic energy conservation error in the collocated mesh scheme 1 errors arising from the interpolations used to estimate the velocity on the cell faces and 2 errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes it is shown that the interpolation error can be eliminated through the use of first order accurate centered interpolation operators with mesh independent weights the pressure error appears to be intrinsic to the scheme and it is shown to scale as o t2 x2 the effects of the conservation errors are investigated numerically through simulations of inviscid flow over an airfoil and in large eddy simulations of turbulent channel flow neither the interpolation error nor the pressure error appear to lead to significant problems in the channel flow simulations where viscous dissipation is present and where the cartesian mesh is stretched in only one direction the inviscid airfoil simulations performed on a curvilinear mesh show a much greater sensitivity to the interpolation error the standard second order centered interpolation is shown to lead to severe numerical oscillations while the kinetic energy conserving first order centered interpolation produces solutions that are almost as smooth as those obtained with a third order upwind interpolation when compared in channel flow simulations however the first order centered interpolation is shown to be far superior to the third order upwind interpolation the latter being adversely affected by numerical dissipation only slight differences were noted when comparing channel flow simulations using first order and second order centered interpolations these results suggest that numerical oscillations can be controlled in curvilinear coordinates through the use of properly constructed non dissipative centered interpolations

existence of multiple periodic orbits of hamiltonian systems on positive type hypersurfaces in r2n abstract this paper deals with the fixed energy problem of hamiltonian systems in r 2n the main result is an existence theorem of multiple periodic orbits for hamiltonian vector fields on a class of contact type but not necessarily star shaped hypersurfaces this is the first multiplicity result for hypersurfaces that are more general than star shaped ones the main result is achieved by using critical point theory for a special hamiltonian function and central gravity of the proof relies on a delicate construction of such hamiltonian function

the g invariant implicit function theorem in infinite dimensions ii our basic theorem is a version of the implicit function theorem in the case of continuous groups of symmetries the result is sufficiently general to cover a great many applications it generalizes some earlier work of the author and corrects and improves some work of vanderbauwhede we also consider the breaking of symmetries problem and the variational case finally we apply our results to study the periodic solutions of an ordinary differential equation

on the fucik spectrum of the laplacian on a torus abstract we study the fucik spectrum of the laplacian on a two dimensional torus t 2 exploiting the invariance properties of the domain t 2 with respect to translations we obtain a good description of large parts of the spectrum in particular for each eigenvalue of the laplacian we will find an explicit global curve in the fucik spectrum which passes through this eigenvalue these curves are ordered and we will show that their asymptotic limits are positive on the other hand using a topological index based on the mentioned group invariance we will obtain a variational characterization of global curves in the fucik spectrum also these curves emanate from the eigenvalues of the laplacian and we will show that they tend asymptotically to zero thus we infer that the variational and the explicit curves cannot coincide globally and that in fact many curve crossings must occur we will give a bifurcation result which partially explains these phenomena

multiple periodic solutions for a semilinear wave equation with nonmonotone nonlinearity on cherche des solutions t periodiques de l equation d onde non lineaire u tt u xx g u u t x u t t x pour t r x 0 u t 0 u t 0 pour t r ou t est un multiple rationnel de et g est une application continument differentiable

transverse ls category for riemannian foliations we study the transverse lusternik schnirelmann category theory of a riemannian foliation f on a closed manifold m the essential transverse category cat e m f is introduced in this paper and we prove that cat e m f is always finite for a riemannian foliation necessary and sufficient conditions are derived for when the usual transverse category cat m f is finite and thus cat e m f cat m f holds a fundamental point of this paper is to use properties of riemannian submersions and the molino structure theory for riemannian foliations to transform the calculation of cat e m f into a standard problem about o q equivariant ls category theory a main result theorem 1 6 states that for an associated o q manifold w we have that cat e m f cat o q hence the traditional techniques developed for the study of smooth compact lie group actions can be effectively employed for the study of the ls category of riemannian foliations a generalization of the lusternik schnirelmann theorem is derived given a c 1 function f m r which is constant along the leaves of a riemannian foliation f the essential transverse category cat e m f is a lower bound for the number of critical leaf closures of f

infinite dimensional linking let n be a closed separable subspace of a hilbert space e we can define a new norm v w satisfying v w v v n and such that the topology induced by this norm is equivalent to the weak topology of n on bounded subsets of n this can be done as follows let ek be an orthonormal basis for n define displaystyle u v w sum k 1 infty frac u e k v e k 2 k quad u v in n

solutions of minimal period for a class of nonconvex hamiltonian systems and applications to the fixed energy problem on considere le systeme hamiltonien jz h z ou j x y y x x y r n r n h est non convexe a un bon comportement superquadratique et satisfait une condition simple reliant ses coefficients de superquadraticite et l exposant dans ce cas on demontre que pour t 0 l existence de solutions pour le systeme hamiltonien de periode minimale t

existence of multiple periodic orbits on star shaped hamiltonian surfaces consider the hamiltonian system hs i 1 n here h c2 2n in this paper we investigate the existence of periodic orbits of hs on a given energy surface z 2n h z c c o is a constant the surface is required to verify certain geometric assumptions bounds a star shaped compact region and for some ellipsoid 2n o o depending in an explicit fashion on the lengths of the main axes of and one other geometrical parameter of such that if furthermore 2 2 1 then hs has at least n distinct geometric orbits on this result is shown to extend and unify several earlier works on this subject among them works by weinstein rabinowitz ekeland lasry and ekeland in proving this result we construct index theories for an s1 action from which we derive abstract critical point theorems for s1 invariant functionals we also derive an estimate for the minimal period of solutions to differential equatious

simple involutive quantales abstract involutive quantales were introduced in 7 as complete lattices equipped with a multiplication and an involution such structures are well known from the calculus of relations the set r el x of binary relations on any setxforms an involutive quantale however the motivating example of an involutive quantale is the spectrum max aof a non commutativec algebraa where max ais the involutive quantale consisting of all closed linear subspaces ofa in 8 it was indeed shown thatacan be reconstructed from the involutive quantale max a demonstrating that involutive quantales do provide a convenient algebraic invariant of non commutativec algebras the aim of this paper is to study involutive quantales from the algebraic point of view our main result is the characterization of simple involutive quantales that is involutive quantales on which the only surjections are isomorphisms or constant morphisms we also show that this class contains all quantales q s of sup preserving endomorphisms on a complete latticeshaving a duality a fortiori all hilbert quantales as defined in 7 a special case of this is r el x which can be seen to be q 2x our investigation of the class of simple involutive quantales is also motivated byc algebras it is proved in 8 that for anyc algebraa max ahas enough homomorphisms into the hilbert quantales q p h where p h is the complete lattice of closed linear subspaces of a hilbert spaceh in this spirit viewing involutive quantales as duals of generalized non commutative topological spaces simple involutive quantales correspond to spaces having only trivial subspaces that is to points we begin a study of those involutive quantales which have enough homomorphisms into simple involutive quantales noting their spatial character such a study has algebraic antecedents in the early work 4 and the more recent work 1 which studied certain lattices noncomplete involutive quantales having enough homomorphisms into simple involutive quantales of the form r el x

etale groupoids and their quantales abstract we establish close and previously unknown relations between quantales and groupoids in particular to each etale groupoid either localic or topological there is associated a unital involutive quantale we obtain a bijective correspondence between localic etale groupoids and their quantales which are given a rather simple characterization and here are called inverse quantal frames we show that the category of inverse quantal frames is equivalent to the category of complete and infinitely distributive inverse monoids and as a consequence we obtain a non functorial correspondence between these and localic etale groupoids that generalizes more classical results concerning inverse semigroups and topological etale groupoids this generalization is entirely algebraic and it is valid in an arbitrary topos as a consequence of these results we see that a localic groupoid is etale if and only if its sublocale of units is open and its multiplication map is semiopen and an analogue of this holds for topological groupoids in practice we are provided with new tools for constructing localic and topological etale groupoids as well as inverse semigroups for instance via presentations of quantales by generators and relations the characterization of inverse quantal frames is to a large extent based on a new quantale operation here called a support whose properties are thoroughly investigated and which may be of independent interest

global bifurcations of critical orbits of g invariant strongly indefinite functionals abstract let h be a separable hilbert space which is an orthogonal representation of a compact lie group g and let h r be a g invariant strongly indefinite functional of the class c 1 to study critical orbits of we have defined the degree for g invariant strongly indefinite functionals which is an element of the euler ring u g using this degree we have formulated the rabinowitz alternative for g invariant strongly indefinite functionals the abstract results are applied to the study of global bifurcations of weak solutions of non cooperative systems of elliptic differential equations

subharmonic solutions with prescribed minimal period for nonautonomous hamiltonian systems on etablit un resultat de multiplicite pour une certaine classe de systemes hamiltoniens periodiques en temps

existence of multiple normal mode trajectories on convex energy surfaces of even classical hamiltonian systems hamiltonian systems of n degrees of freedom for which the hamiltonian is a function that is even both in its joint n coordinate variables as well as in its joint n momentum variables are discussed for such systems the number of distinct trajectories which correspond to particular periodic solutions normal modes with the same energy is investigated to that end a constrained dual action principle is introduced applying min max methods to this variational problem several results are obtained among which the existence of at least n distinct trajectories if specific conditions are satisfied

morse indices of critical manifolds generated by min max methods with compact lie group actions and applications we derive some upper and lower bounds for morse indices of critical manifolds generated by min max principles for functionals invariant under a general compact lie group or a finite group action the results generalize the similar results in the nonequivariant no group action case in doing so we also generalize the extension theorem of dugundji type in the nonequivariant case to the equivariant group action case as an application we obtain a precise growth estimate for the whole sequence of critical values given by the min max procedure for some superquadratic second order differential equations it is well known that this growth estimate is crucial in showing the existence of multiple solutions of some superquadratic perturbed hamiltonian systems and equations

periodic solutions to second order hamiltonian systems in an unbounded potential well in this paper we give some results on the existence of periodic solutions to the second order hamiltonian system where and is an open set of n with non empty bounded complement n we suppose v t x is periodic in t v t x as x and v is super or sub quadratic as x

nuclei and conuclei on residuated lattices in this paper we investigate some properties of nuclei and conuclei on residuated lattices and their concrete structures by means of nuclei and conuclei we give the respective characterizations for a residuated lattice reducing to a generalized mv algebra and a generalized bl algebra based on studying regular commutative bounded integral residuated lattices we introduce the concept of a pseudo dual quantale and investigate some properties of it and prove that the set of fuzzy sets of a nonempty set equipped with multiplication and negation operations is a commutative girard quantale finally we discuss the relationship between quantic nuclei and quantic conuclei on a pseudo dual quantale and show that the quantic nuclei and the ideal conuclei on a pseudo girard quantale are in one to one correspondence

a semilinear schrodinger equation in the presence of a magnetic field we consider the semilinear stationary schrodinger equation in a magnetic field i a 2u v x u g x u u in n where v is the scalar or electric potential and a is the vector or magnetic potential we study the existence of nontrivial solutions both in the critical and in the subcritical case respectively g x u u 2 2 and g x u c 1 u p 2 where 2 p 2 the results are obtained by variational methods for g critical we use constrained minimization and for subcritical g we employ a minimax type argument in the latter case we also study the existence of infinitely many geometrically distinct solutions

multiple solutions for noncooperative p x laplacian equations in rn involving the critical exponent abstract in this paper we study the multiplicity of solutions for a class of noncooperative p x laplacian equations in r n involving the critical exponent by using the limit index theory due to li y q li a limit index theory and its application nonlinear anal 25 1995 1371 1389 and concentration compactness principle we obtain a sequence of radially symmetric solutions

an homotopical index and multiplicity of periodic solutions to dynamical systems with singular potential this paper has two main purposes the first one is to define a tool homotopical index theory which provides critical points for functionals having a singularity and a lack of compactness the second one is to apply the abstract results in order to find a multiplicity of periodic solutions to a class of dynamical systems with singular potential let us fix up some notations in the following t 0 will be fixed and we shall denote hj h r tz w and en the subspace of hf of all the constant functions we consider

existence and multiplicity of solutions for fourth order elliptic equations of kirchhoff type with critical growth in ℝn in this paper we deal with the existence and multiplicity of solutions for fourth order elliptic equations of kirchhoff type with critical nonlinearity e 4 2 u e 4 a b r n u 2 d x u v x u u 2 2 u h x u t x n by using lions second concentration compactness principle and concentration compactness principle at infinity to prove that ps condition holds locally and by variational method we prove that it has at least one solution and for any m it has at least m pairs of solutions

multiple solutions for a semilinear elliptic equation let ql be a bounded smooth domain in rn n 1 we consider the problem of finding nontrivial solutions to the elliptic boundary value problem au au h x iuip lu in q u 0 onoq where h 0 h 0 is holder continuous on q and p 1 a are constants let qlo denote the interior of the set where h vanishes in q we assume h 0 a e on q k1o and consider the eigenvalues ai k2 and ai 0o of the dirichlet problem in q and qlo respectively we prove that no nontrivial solution of the equation exists if a satisfies for some k 1 ak 90 k 1 a satisfies as ql 1 we consider the problem of finding nontrivial solutions to the elliptic boundary value problem 0 1 au au h x iuip u in q 0 2 u 0 on aq where h is a nonnegative not identically zero holder continuous function defined on q and p 1 a are constants ouyang 5 studied existence and uniqueness of positive solutions to problem 0 1 0 2 and also of its corresponding analogue on a compact riemannian manifold that paper mainly focused on studying the effect of vanishing of the received by the editors october 13 1993 and in revised form october 24 1994 1991 mathematics subject classification primary 35j25 35j20

a new reynolds stress algebraic equation model a new reynolds stress algebraic equation modeltsan hsing shih and jiang zhucenter for modeling of turbulence and transitioninstitute for computational mechanics in propulsionnasa lewis research center cleveland ohiojohn l lumleycornell university ithaca new yorkabstracta general turbulent constitutive relation shih and lumley 1993 is directly appliedto propose a new reynolds stress algebraic equation model in the development of thismodel the constraints based on rapid distortion theory and realizability i e the positivityof the normal reynolds stresses and the schwarz inequality between turbulent velocitycorrelations are imposed model coefficients are calibrated using well studied basic flowssuch as homogenous shear flow and the surface flow in the inertial sublayer the performanceof this model is then tested in complex turbulent flows including the separated flow over abackward facing step and the flow in a confined jet the calculation results are encouragingand point to the success of the present model in modeling turbulent flows with complexgeometries 1 introductionthe present study concentrates on complex turbulent shear flows which are of greatinterest in propulsion systems the particular flows presented in this paper are for thebackward facing step and the confined jet both of which have complex structures forexample a confined jet combines several types of flow structure and flow phenomena suchas a shear layer jet recirculation separation and reattachment accurate prediction ofthese flows is of great importance in all the key elements of engine design the turbulence model developed in this study is a reynolds stress algebraic equationmodel which is based on a turbulent constitutive relation shill and lum ey 1993 a result ofrapid distortion theory reynolds 1987 and the turbulent realizability principle schumann1977 lumley 1978 the constitutive relation is obtained using the invariance theory incontinuum mechanics for flows including a passive scalar this theory leads to a generalconstitutive relation for the reynolds stress tensor uiuj in terms of the mean deformationrate tensor ui j and the turbulent velocity and length scales characterized by the turbulentkinetic energy k and its dissipation rate s pope 1975 applied a similar constitutiverelation to rodi s algebraic reynolds stress formulation rodi 1972 in conjunction withthe lrr second order closure model launder et ai 1975 and obtained an explicit algebraic

a note on the minimal periodic solutions of nonconvex superlinear hamiltonian system in this paper we consider the multiplicity result of minimal periodic solutions for the first order hamiltonian system email protected t email protected h x t we point out a mistake in the literatures m girardi m matzeu solutions of minimal period for a class of nonconvex hamiltonian systems and applications to the fixed energy problem nonlinear anal t m a 10 4 1986 371 382 and tianqing an on the minimal periodic solutions of nonconvex superlinear hamiltonian systems j math anal appl 329 2007 1273 1284 when the potential is even under some stronger restricted conditions we give the correct proof and obtain more distinct nonconstant periodic solutions with minimal period t

morse theory for symmetric functionals on the sphere and an application to a bifurcation problem abstract this paper uses conley s index to study the cortical points of a function f on a finite dimensional sphere in presence of a symmetry group the authors prove a theorem which leads to a lower bound on the number of critical points of f when the group is finite even if the action is not free this investigation has been motivated by the following bifurcation problem au lambda where a is a variational g equivariant operator an estimated on the number of branches bifurcating from an eigenvalue of a 0 is given author

a z p borsuk ulam theorem and index theory with a multiplicity result in partial differential equations on demontre un theoreme de borsuk ulam z p generalise c est le resultat topologique essentiel pour developper un theoreme d indice z p on demontre un resultat de multiplicite pour un systeme d equations aux derivees partielles elliptiques non lineaires

sup lattice 2 forms and quantales a 2 form between two sup lattices l and r is defined to be a sup lattice bimorphism l r 2 such 2 forms are equivalent to galois connections and we study them and their relation to quantales involutive quantales and quantale modules as examples we describe applications to c algebras

analytical mini max methods for hamiltonian brake orbits of prescribed energy on considere des caracterisations explicites de solutions periodiques de systemes hamiltoniens autonomes d ordre 2 de la forme q v q q t r n ou le potentiel v satisfait les conditions suivantes v c 2 r n v x v o 0 v est strictement convexe sur r n

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

geometric multigrid with applications to computational fluid dynamics an overview is given of the development of the geometric multigrid method with emphasis on applications in computational fluid dynamics over the last ten years both compressible and incompressible flow problems and their corresponding multigrid solution methods are discussed the state of the art is described with respect to methods employed in industry as well as the multigrid efficiency obtained in academic applications

a collocated method for the incompressible navier stokes equations inspired by the box scheme we present a new finite difference numerical method to solve the incompressible navier stokes equations using a collocated discretization in space on a logically cartesian grid the method shares some common aspects with and it was inspired by the box scheme it uses centered second order accurate finite difference approximations for the spatial derivatives combined with semi implicit time integration the proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity pressure form of the equations the continuity equation is enforced exactly to machine accuracy at the collocated locations whereas the momentum equations are evaluated in a staggered manner this formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure the method shows uniform order of accuracy both in space and time for velocity and pressure in addition the skew symmetric form of the non linear advection term of the navier stokes equations improves discrete conservation of kinetic energy in the inviscid limit to within the order of the truncation error of the time integrator the method has been formulated to accommodate different types of boundary conditions fully periodic periodic channel inflow outflow and lid driven cavity always ensuring global mass conservation a novel aspect of this finite difference formulation is the derivation of the discretization near boundaries using the weak form of the equations as in the finite element method the method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver to assess the applicability of the new method presented in this paper four realistic flow problems have been simulated and results are compared with those in the literature these cases include a lid driven cavity backward facing step kovasznay flow and fully developed turbulent channel

solutions for a class of quasilinear choquard equations with hardy littlewood sobolev critical nonlinearity abstract in this article we consider the quasilinear choquard equation with critical nonlinearity in r n e 2 u v x u e 2 u u 2 r n u 2 2 x y d y u 2 2 2 u h x u u where 0 n n 3 2 2 n n 2 is the critical exponent in the sense of hardy littlewood sobolev inequality e is a real parameter by using a change of variables the quasilinear equations are reduced to a semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem under suitable assumptions on v and h we investigate the existence and multiplicity of solutions for the above problem by using the mountain pass theorem and index theory in order to overcome the lack of compactness we apply the concentration compactness principle