multiple steady states in phytoplankton population induced by photoinhibition abstract we study the effect of photoinhibition in a nonlocal reaction diffusion advection equation which models the dynamics of a single phytoplankton species in a water column where the growth of the species depends solely on light our results show that in contrast to the case of no photoinhibition where at most one positive steady state can exist the model with photoinhibition possesses at least two positive steady states in certain parameter ranges our approach involves bifurcation theory and perturbation reduction arguments

infinitely many solutions of p sublinear p laplacian equations abstract existence of infinitely many solutions of the p laplacian equation p u a x u q 2 u f x u u w 0 1 p is proved where 1 q p r n is a bounded domain with smooth boundary a c is allowed to change sign and f c for some 0 is a perturbation term which may not be odd in u

existence and multiplicity of solutions for a discontinuous problems with critical sobolev exponents abstract in this paper we consider the equation p u u p 2 u f x u in r n with discontinuous nonlinearity where 1 p n 0 is a real parameter and p n p n p is the critical sobolev exponent under proper conditions on f applying the nonsmooth critical point theory for locally lipschitz functionals we obtain at least one nontrivial nonnegative solution provided that 0 and for any k n it has k pairs of nontrivial solutions if k where 0 and k are positive numbers in particular we obtain the existence results for f is discontinuous in just one point

critical point theory for nonsmooth functionals abstract in this paper we develop critical point theory for nonsmooth functional f h 0 1 r defined by f u 1 2 i j 1 a i j x u d i u d j u d x g x u d x the corresponding deformation lemmas are proved with the application to the bifurcation for quasilinear schrodinger equations in mind we extend the obtained results to that for a functional defined on a product space and prove a generalized saddle point theorem

nonlinear riemann hilbert problem for bordered riemann surfaces let be a bordered riemann surface with genus g and m boundary components let z z be a smooth family of smooth jordan curves in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i which all contain the point 0 in their interior then there exists a holomorphic function f z on smooth up to the boundary with at most 2 g m 1 zeros on such that f z z for every z

infinitely many solutions for a differential inclusion problem in r n abstract in this paper we consider the differential inclusion problem di p u u p 2 u x f u x x r n u w 1 p r n where 2 n p l 1 r n l r n is radially symmetric and f stands for the generalized gradient of a locally lipschitz function f r r under suitable oscillatory assumptions on the potential f at zero or at infinity we show the existence of infinitely many radially symmetric solutions of di no symmetry requirement on f is needed our approach is based on a non smooth ricceri type variational principle developed by marano and motreanu j differential equations 182 2002 108 120

the monotone iterative technique for a parabolic boundary value problem with discontinuous nonlinearity let be a bounded lebesgue measurable domain of r n with a lipschitz boundary the following initial boundary value problem is considered u t lu f u h in q bu o on u 0 where q o t o t and 0 0 l is a uniformly elliptic operator b a boundary operator defined by bu u v bu in which v denotes the outer normal derivative on and f represents a discontinuous non linearity

tracking pattern evolution through extended center manifold reduction and singular perturbations in this paper we develop an extended center manifold reduction method a methodology to analyze the formation and bifurcations of small amplitude patterns in certain classes of multi component singularly perturbed systems of partial differential equations we specifically consider systems with a spatially homogeneous state whose stability spectrum partitions into eigenvalue groups with distinct asymptotic properties one group of successive eigenvalues in the bifurcating group are widely interspaced while the eigenvalues in the other are stable and cluster asymptotically close to the origin along the stable semi axis the classical center manifold reduction provides a rigorous framework to analyze destabilizations of the trivial state as long as there is a spectral gap of sufficient width when the bifurcating eigenvalue becomes commensurate to the stable eigenvalues clustering close to the origin the center manifold reduction breaks down moreover it cannot capture subsequent bifurcations of the bifurcating pattern through our methodology we formally derive expressions for low dimensional manifolds exponentially attracting the full flow for parameter combinations that go beyond those allowed for the classical center manifold reduction i e to cases in which the spectral gap condition no longer can be satisfied our method also provides an explicit description of the flow on these manifolds and thus provides an analytical tool to study subsequent bifurcations our analysis centers around primary bifurcations of transcritical type that can be either of co dimension 1 or 2 in two and three component pde systems we employ our method to study bifurcation scenarios of small amplitude patterns and the possible appearance of low dimensional spatio temporal chaos we also exemplify our analysis by a number of characteristic reaction diffusion systems with disparate diffusivities

existence results for obstacle problems for nonlinear hemivariational inequality at resonance in this paper we are interested in studying the existence of solutions to obstacle problems for nonlinear hemivariational inequality at resonance driven by the p laplacian using a variational approach based on the nonsmooth critical point theory for nondifferentiable functionals we prove two existence theorems

nonlinear hemivariational inequalities at resonance in this paper we examine a semilinear hemivariational inequality at resonance in the first eigenvalue 1 of h01 z we prove two existence theorems for such problems our approach is variational and is based on the nonsmooth critical point theory of chang which uses the subdifferential calculus of clarke for locally lipschitz functions

on the solvability of some discontinuous third order nonlinear differential equations with two point boundary conditions abstract we prove the existence of extremal solutions for the third order discontinuous functional nonlinear problem u t f t u u t u t for a e t a b u a a a r l 1 u u u a u b u a 0 l 2 u u a u b u b 0 by using a fixed point theorem after having established some existence results for some auxiliary second order nonlinear problems we observe that together with the discontinuities allowed on the spacial variable u with adequate modifications of technical type analogous results can be obtained when the equation has a second member not necessarily continuous in u

polynomially convex hulls with piecewise smooth boundaries is the boundary of a compact convex set y z c c m with nonempty interior set y u z x y z alexander and wermer 1 and slodkowski 8 proved zcbd independently that each point p in the polynomial convex hull of m n p d lies in the graph of a bounded analytic disk f z z f 1 z f z f j h d for l j m with image in 3 r alexander and wermer obtained a more precise information in the case when m 1 and each fiber m z is a circle 1 theorems 2 and 3 in this paper we shall assume the existence of an analytic disk f o z z f0 z on d continuous on such thatfo z is an interior point of y z for each z bd then each bounded analytic disk f z z f z in ai which passes through a boundary point of a r lying over d is entirely contained in the boundary o fair and its cluster set f d f d is contained in m theorem 1 1 if m 1 and m is a smooth submanifold of r as above then the hull 3 r has piecewise smooth boundary and is f dled by the images of analytic disks with smooth boundary values contained in m theorem 1 2 we also obtain a uniqueness result for the representing measures corollary 1 3

on a class of boundary value problems involving the p biharmonic operator abstract a nonlinear boundary value problem involving the p biharmonic operator is investigated where p 1 it describes various problems in the theory of elasticity e g the shape of an elastic beam where the bending moment depends on the curvature as a power function with exponent p 1 we prove existence of solutions satisfying a quite general boundary condition that incorporates many particular boundary conditions which are frequently considered in the literature

iterative solutions for a beam equation with nonlinear boundary conditions of third order a fourth order differential equation with nonlinear boundary conditions modeling beams on elastic foundations is considered iterative solutions are proved through the contraction principle some numerical simulations are also provided

monotone positive solutions for a fourth order equation with nonlinear boundary conditions abstract this work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions the results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions numerical simulations are also presented

oscillating solutions of a nonlinear fourth order ordinary differential equation we study the existence of periodic solutions for a nonlinear fourth order ordinary differential equation under suitable conditions we prove the existence of at least one solution of the problem applying coincidence degree theory and the method of upper and lower solutions

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

iterative methods for discrete nonlinear riemann hilbert problems abstract let d denote the complex unit disk t d and let f t r 2 r be a given function the paper presents iterative methods for the computation of functions w u iv which are holomorphic in d and satisfy the boundary relation f t u t v t 0 for all t t it is shown that an appropriate discretization of this boundary value problem can be obtained by replacing the class of holomorphic functions with the set of polynomials of degree not exceeding n and imposing the boundary condition at a grid of 2n uniformly distributed points on the circle t the proposed iterative methods for the solution of the discrete as well as the nondiscrete problems converge quadratically in a neighborhood of the solution error estimates for the iterative solutions are given in the scale of the sobolev spaces wk2

simulation of three dimensional phytoplankton dynamics comptetion in light limited environments in this paper we develop computational methods for a three dimensional model of competition for light between phytoplankton species the competing phytoplankton populations are exposed to both horizontal and vertical mixing the vertical light dependence of phytoplankton photosynthesis implies that the three dimensional model is formulated in terms of integro partial differential equations that require an efficient numerical solution technique due to the stiffness of the discretized system we select an implicit integration method however the resulting implicit relations are extremely expensive to solve caused by the strong coupling of the components this coupling originates from the three spatial dimensions the interaction of the various species and the integral term to reduce the amount of work in the linear algebra part we use an approximate matrix factorization technique the performance of the complete algorithm is demonstrated on the basis of two test examples it turns out that unconditional stability i e a stability is a very useful property for this application

closed geodesics with lipschitz obstacle abstract geodesics on a general subsetmof r nare considered whenmis the closure of an open subset with lipschitz boundary and suitable topological conditions are fulfilled the existence of a nonconstant closed geodesic is proved

complex interpolation of normed and quasinormed spaces in several dimensions i a variety of complex interpolation methods for families of normed or quasi normed spaces parametrized by points of domains in complex homo geneous spaces parametrized by points of domains in complex homogeneous spaces is developed results on existence continuity uniqueness reiteration and duality for interpolation are proved as well as on interpolation of oper ators a minimum principle for plurisubharmonic functions is obtained and used as a tool for the duality theorem

existence and multiplicity of solutions for a class of forced vibration problems with obstacles abstract by variational methods an existence theorem and two multiplicity theorems of solutions of the following forced vibration problems are obtained 1 1 x q x x 2 g t x f t with 1 2 x 0 x 2 x 0 x 2 0 x t 0 t r and 1 3 x t 0 x t 0 if x t 0 0 where x t 0 lim t t 0 0 x t x t 0 lim t t 0 0 x t

solutions and multiple solutions for periodic systems with nonhomogeneous differential operators abstract in this paper we consider nonlinear periodic systems driven by the nonhomogeneous vector p laplacian differential operator and with a nonsmooth potential using variational techniques based on the nonsmooth critical point theory we prove existence and multiplicity results finally we obtain an existence result for systems driven by the ordinary vector p laplacian and we show that it is still true in the more general framework of the previous results

elliptic equations with indefinite concave nonlinearities near the origin in this note existence of infinitely many solutions is proved for an elliptic equation with indefinite concave nonlinearities

on the existence of small energy solutions for a sublinear neumann problem abstract in this paper we are concerned with the sublinear problem 0 1 u u p 2 u in u 0 on where r n is a bounded domain and 1 p 2 for p 1 the nonlinearity u p 2 u will be identified by sgn u in contrast to previous work on the dirichlet problem some difficulties arise due to the fact that the associated energy functional is not bounded from below complementing recent work by parini and weth in 15 on least energy solutions we prove that 0 1 has infinitely many solutions with small negative energy

polynomial hulls and h infty control for a hypoconvex constraint we say that a subset of mathbb c n is hypoconvex if its complement is the union of complex hyperplanes let delta be the closed unit disk in mathbb c gamma partial delta we prove two conjectures of helton and marshall let rho be a smooth function on gamma times mathbb c n whose sublevel sets have compact hypoconvex fibers over gamma then with some restrictions on rho if y is the set where rho is less than or equal to 1 the polynomial convex hull of y is the union of graphs of analytic vector valued functions with boundary in y furthermore we show that the infimum inf f in h infty delta n rho z f z infty is attained by a unique bounded analytic f which in fact is also smooth on gamma we also prove that if rho varies smoothly with respect to a parameter so does the unique f just found

a theory of complex interpolation for families of banach spaces abstract a detailed development is given of a theory of complex interpolation for families of banach spaces which extends the well known theory for pairs of spaces

extremal discs and the regularity of cr mappings in higher codimension we develop a local theory of extremal analytic discs attached to a strictly pseudoconvex manifold of higher codimension in complex space we then apply the results to prove the regularity of cr homeomorphisms of such manifolds introduction in his celebrated paper lempert li introduced extremal analytic discs as geodesies of the kobayashi metric on a convex domain d c cn let a be the unit disc in the complex plane an analytic disc a d is called extremal if 0 attains its maximum among all analytic discs in d with the same values and directions at 0 g a extremal discs are important holomorphic invariants of d their boundaries lie in the boundary bd of the domain and form an invariant family of curves for the cr structure of bd lempert li l2 applies the extremal discs to the regularity of biholomorphic mappings monge amp re equations and normal forms of convex domains other applications include deformations and embeddibility of cr structures bl bd and polynomial hulls s

existence of solutions for elliptic hemivariational inequalities abstract this paper is devoted to the existence of solutions concerning the dirichlet problem for quasilinear elliptic hemivariational inequalities at the first eigenvalue using the notion of the generalized gradient of clarke and the property of the first eigenfunction some existence results of solutions have been proved

on a free boundary problem abstract in this paper we will be concerned with the existence of positive solutions of the following discontinuous problem p u f u h u in u h on where is the unit ball of r n n 3 and h is the heaviside function the problem is written in an equivalent integral equation form the shape of the free boundary problem x u x is studied for when is a positive real parameter f and h are given functions

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

multiple solutions of sublinear elliptic equations with small perturbations abstract we study the sublinear elliptic equation having two nonlinear terms where the main term f x u is sublinear and odd with respect to u and the perturbation term is any continuous function with a small coefficient then we prove the existence of multiple small solutions

local c1 ω minimizers versus local w1 p ω minimizers of nonsmooth functionals abstract we study not necessarily differentiable functionals of the form j u 1 p u p d x 1 p u p d x j 1 x u d x j 2 x u d with 1 p involving locally lipschitz functions j 1 r r as well as j 2 r r we prove that local c 1 minimizers of j must be local w 1 p minimizers of j

dynamic contact problem for viscoelastic piezoelectric materials with normal damped response and friction in this paper we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential the contact is modeled by a general normal damped response condition and a friction law which are nonmonotone possibly multivalued and have the subdifferential form the existence of a weak solution to the model is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

periodic solutions for second order differential equations with discontinuous restoring forces we deal with the existence of periodic solutions for problems with a jump discontinuity we use an approximation procedure and the method of the lower and upper solutions

existence of solutions for dirichlet elliptic problems with discontinuous nonlinearity abstract in this paper we concern with definite sign and sign changing solutions of a class of discontinuous problems by using the dual method we overcome the difficulty of non differentiability and obtain the existence results of definite sign solution and a sign changing solutions on the nehari manifold for the discontinuous problems some continuous results are extended to the discontinuous cases

polynomial hulls with convex fibers and complex geodesics let x be a compact subset of z 1 cn with convex fibers several equivalent conditions are obtained that characterize polynomially convex hulls y x with nonempty interior under the latter assumption it is shown that every z0 w0 y and such that z0 1 is contained in a closed n dimensional complex submanifold of d cn which is tangent to y along an analytic disc we show as an application that some results of lempert on complex geodesies in convex domains are direct consequences of properties of polynomial hulls

on bounded analytic functions in finitely connected domains a new proof of the corona theorem for finitely connected domains is given it is based on a result on the existence of a meromorphic selection from an analytic set valued function the latter fact is also applied to the study of finitely generated ideals of h over multiply connected domains introduction in this paper which is a direct continuation of 18 we study applications of analytic multifunctions to some topics in function theory on finitely connected domains related mainly to the corona problem concerniag analytic multifunctions which are certain set valued functions cf definition 1 2 1 3 of 18 form sufficient background for our purposes here the reader is also referred there for the information about the origin of the approach employed in this paper however basic definitions and references are provided below our basic new result theorem 1 4 associates to every analytic multifunction defined in a finitely connected domain some meromorphic functions with poles at the critical points of green s function of this domain some improvements of this fact in txhe special case of an annulus are discussed in 3 this main technical result is applied in 2 to help obtain a new simple proof of the well known corona theorem for finitely connected domains a novel feature of this proof as compared with e g forelli 9 stout 19 gamelin 7 is that it does not use the corresponding result for the unit disc the same methods are used in 4 where we consider the question when some power of g from h g belongs to the ideal af1 af2 afn we obtain generalizations to multiply connected domains of a result due to t wolff theorems 4 1 and 4 2 as well as its refinements in the case of the unit disc corollary 4 4 and example 5 3 all proofs given in this paper extend to finite riemann surfaces 1 a meromorphic selection theorem the main result of this section relates some meromorphic vector valued functions to analytic multifunctions defined in finitely connected domains first we recall some definitions definition 1 1 folk a locally compact set z c cn is a maximum set if for every compact set n c z and for every analytic function f defined in a neighborhood of n the inequality maxn if l maxazn if l holds definition 1 2 16 18 anuppersemicontinuousset valuedcorrespondence z k z g 2c where g c c is open and all k z are nonempty and received by the editors january 16 1986 presented to the society special session on convex analysis new orleans january 11 1986 1980 mathematics subject classifiratson 1985 ren primary 32a80 32e20 46j15 2 1987 american mathematical society 0002 9947 87 1 00 25 per page

blooming in a nonlocal coupled phytoplankton nutrient model recently it has been discovered that the dynamics of phytoplankton concentrations in an ocean exhibit a rich variety of patterns ranging from trivial states to oscillating and even chaotic behavior j huisman n n pham thi d m karl and b p sommeijer nature 439 2006 pp 322 325 this paper is a first step towards understanding the bifurcational structure associated with nonlocal coupled phytoplankton nutrient models as studied in that paper its main subject is the linear stability analysis that governs the occurrence of the first nontrivial stationary patterns the deep chlorophyll maxima dcms and the benthic layers bls since the model can be scaled into a system with a natural singularly perturbed nature and since the associated eigenvalue problem decouples into a problem of sturm liouville type it is possible to obtain explicit and rigorous bounds on and accurate approximations of the eigenvalues the analysis yields bifurcation manifolds in parameter space of which the existence position and nature are confirmed by numerical simulations moreover it follows from the simulations and the results on the eigenvalue problem that the asymptotic linear analysis may also serve as a foundation for the secondary bifurcations such as the oscillating dcms exhibited by the model

existence of solutions for wave type hemivariational inequalities with noncoercive viscosity damping abstract in this paper we prove the existence of solutions for a hyperbolic hemivariational inequality of the form u au bu j u f where b is a linear elliptic operator and a is linear and nonnegative not necessarily coercive

elliptic problems with discontinuities in this paper we prove two existence theorems for elliptic problems with discontinuities the first one is a noncoercive dirichlet problem and the second one is a neumann problem we do not use the method of upper and lower solutions for neumann problems we assume that f is nondecreasing we use the critical point theory for locally lipschitz functionals

periodic problems with asymmetric nonlinearities and nonsmooth potentials abstract we consider a nonlinear periodic boundary value problem driven by the ordinary scalar p laplacian and with a nonsmooth locally lipschitz potential which exhibits an asymmetric behaviour at and at using the fucik spectrum and a variational approach based on the nonsmooth critical point theory we obtain a solution for the problem using a general minimax principle concerning linking sets

on some elliptic hemivariational and variational hemivaritional inequalities abstract the existence of solutions to an elliptic hemivariational inequality involving the p laplacian is first established the variational hemivariational case which includes the above one is then examined when p 2 both of them are chiefly treated through mountain pass like critical point results for non differentiable functions

a fixed point operator for a nonlinear boundary value problem we study a semilinear second order equation with a nonlinear boundary condition for the axial deformation of a nonlinear elastic beam in the presence of friction under appropriate conditions we define a fixed point operator in order to obtain solutions for this equation

nonlinear algebraic systems with discontinuous terms abstract using a multiple critical points theorem for locally lipschitz continuous functionals we establish the existence of at least three distinct solutions for a parametric discrete differential inclusion problem involving a real symmetric and positive definite matrix applications to tridiagonal fourth order and partial difference inclusions are presented

the dual variational principle and elliptic problems with discontinuous nonlinearities on etudie des problemes aux valeurs limites elliptiques du type u f u p x x u 0 x ou r n est un domaine borne et f peut avoir des discontinuites on cherche des solutions en utilisant le principe d action duale de clarke

a variational approach to discontinuous problems with critical sobolev exponents abstract we employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form u h x h u a uq u2 1 in rn where a 0 are parameters h x is both nonnegative and integrable on rn h is the heaviside function 2 is the critical sobolev exponent and 0 q

existence theorems for noncoercive elliptic problems with discontinuous nonlinearities abstract in this paper we are interested for elliptic problems of ambrosetti prodi type with discontinuous nonlinearities the differential operator is the p laplacian and we use a variational method for locally lipschitz functionals due to chang we do not use the method of upper and lower solution and we do not suppose any monotonicity condition on the right hand side

infinitely many solutions for a class of sublinear schrodinger equations with indefinite potentials in this paper we are concerned with qualitative properties of entire solutions to a schrodinger equation with sublinear nonlinearity and sign changing potentials our analysis considers three distinct cases and we establish sufficient conditions for the existence of infinitely many solutions

nonsmooth critical point theory on closed convex sets and nonlinear hemivariational inequalities abstract in this paper we develop a critical point theory for nonsmooth locally lipschitz functionals defined on a closed convex set extending this way the work of struwe variational methods springer berlin 1990 through a deformation result we obtain minimax principles producing critical points then we use the theory to obtain positive and negative solutions of nonlinear and semilinear hemivariational inequalities in this context we improve a result on positive solutions for semilinear elliptic problems due to nirenberg variational methods in nonlinear problems in topics in calculus of variations lecture notes in mathematics vol 1365 springer berlin 1987

boundary value problems for discontinuous perturbations of singular ϕ laplacian operator abstract systems of differential inclusions of the form u f t u t 0 t where with strictly convex is a homeomorphism of the ball b a r n onto r n are considered under dirichlet periodic and neumann boundary conditions here f t x stands for the generalized clarke gradient of f t at x r n using nonsmooth critical point theory we obtain existence results under some appropriate conditions on the potential f examples of applications concerning filippov type solutions are also provided

existence and location results for hinged beam equations with unbounded nonlinearities abstract this work presents some existence non existence and location results for the problem composed by the fourth order fully nonlinear equation u 4 x f x u x u x u x u x s p x for x 0 1 where f 0 1 r 4 r and p 0 1 r are continuous functions and s is a real parameter with the lidstone boundary conditions u 0 u 1 u 0 u 1 0 this problem models several phenomena such as the bending of an elastic beam simply supported at the endpoints the arguments used apply a lower and upper solutions technique a priori estimations and topological degree theory in this paper we replace the usual bilateral nagumo condition by some one sided conditions which enables us to consider unbounded nonlinearities

nonsmooth version of fountain theorem and its application to a dirichlet type differential inclusion problem abstract in this paper we establish a nonsmooth version of fountain theorem by adopting the framework of nonsmooth analysis theory which is a generalization of theorem 3 6 of willem 1996 2 then we present an application of this theorem to a dirichlet type differential inclusion problem

a shooting method for a nonlinear beam equation abstract we study the existence of solutions for a nonlinear fourth order ode with nonlinear boundary condition that arises in beam theory using a shooting type argument we prove the existence of at least one solution of the problem

the dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation the dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation m r grossinho a b 1 st a tersian c 2 a departamento de matem atica iseg universidade t ecnica de lisboa rua do quelhas 6 1200 lisboa portugal b cmaf universidade de lisboa av prof gama pinto 2 1699 lisboa codex portugal c center of applied mathematics and informatics university of rousse 8 studentska str 7017 rousse bulgaria

existence and uniqueness results for the bending of an elastic beam equation at resonance etude d un probleme non lineaire aux valeurs limites pour la flexion d une poutre elastique en appui simple aux deux extremites dans le cas de resonance theoremes d existence et d unicite

surjection and inversion for locally lipschitz maps between banach spaces abstract we study the global invertibility of non smooth locally lipschitz maps between infinite dimensional banach spaces using a kind of palais smale condition to this end we consider the chang version of the weighted palais smale condition for locally lipschitz functionals in terms of the clarke subdifferential as well as the notion of pseudo jacobians in the infinite dimensional setting which are the analog of the pseudo jacobian matrices defined by jeyakumar and luc using these tools we obtain the existence and uniqueness of solution for certain nonlinear equations defined by locally lipschitz mappings along the way we also obtain a global surjection theorem for locally lipschitz maps in terms of pseudo jacobians

periodic solutions to hamiltonian inclusions abstract we prove the existence of periodic trajectories of hamiltonian inclusions which reduce to the usual hamiltonian equations in the presence of smoothness this is accomplished via a direct variational principle involving a new action integral in an extended sense

on a nonsmooth fourth order boundary value problem abstract existence of solutions of the following boundary value problem is investigated by a variational approach u i v a u b u f t u u 0 a u 0 u 1 a u 1 u 0 u 1 j u 0 u 1 u 0 u 1 here f t 0 1 r r is a caratheodory mapping locally lipschitz with respect to the second variable and f t denotes the generalized clarke gradient of f t with respect to while j is assumed to be a proper convex lower semicontinuous function whose subdifferential is denoted by j this problem is a model for real beam shell applications

lower and upper solutions for a fully nonlinear beam equation abstract in this paper the two point fourth order boundary value problem is considered u i v f t u u u u 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r 4 r is a continuous function satisfying a nagumo type condition we prove the existence of a solution lying between lower and upper solutions using an a priori estimation lower and upper solutions method and degree theory the same arguments can be used with adequate modifications for any type of two point boundary value problem including all derivatives until order three with the second and the third derivatives given in different end points an application to the extended fisher kolmogorov problem will be obtained

second and higher order systems of boundary value problems abstract existence results for systems of kth order boundary value problems are presented our analysis is based on a nonlinear alternative of a granas and use of a priori bounds