surrogate programming and multipliers in quasi convex programming a result due to luenberger on the existence of multipliers in a quasi convex programming problem is extended to the case of constraints given by an arbitrary convex cone under a constraint qualification condition more general than slater s condition the existence of solutions is not assumed we point out links with even convexity in the sense of fenchel and quasi subdifferentiability in the sense of greenberg pierskalla and we observe that the couples of primal dual optimal solutions reduce to saddle points of a suitable lagrangian function

analyzing linear systems containing strict inequalities via evenly convex hulls the evenly convex hull of a given set is the intersection of all the open halfspaces which contain such set hence the convex hull is contained in the evenly convex hull this paper deals with finite dimensional linear systems containing strict inequalities and possibly weak inequalities as well as equalities the number of inequalities and equalities in these systems is arbitrary possibly infinite for such kind of systems a consistency theorem is provided and those strict inequalities weak inequalities equalities which are satisfied for every solution of a given system are characterized such results are formulated in terms of the evenly convex hull of certain sets which depend on the coefficients of the system

on nontrivial solutions of a dirichlet problem whose jumping nonlinearity crosses a multiple eigenvalue let be a bounded domain in rn n 2 with smooth boundary let p r r be a continuous function such that p 0 0 and limt p t t p exist we discuss the existence of nontrivial solutions of the dirichlet problem u p u in u 0 on our hypotheses relate the position of the point p p in the plane with the extended spectrum of they seem to allow noticeably greater freedom for the numbers p than is usually found in the literature in the sense that the interval with end points p is here permitted to contain in its interior an eigenvalue of arbitrarily multiplicity of it also appears that we significantly weaken some technical conditions on p of another paper which treats the crossing of a simple eigenvalue

complete monotone quasiconcave duality we introduce a notion of complete monotone quasiconcave duality motivated by some economic applications we show that this duality holds for important classes of quasiconcave functions

on the approximate solutions of fragmentation equations a numerical model based on the finite volume scheme is proposed to approximate the binary breakage problems initially it is considered that the particle fragments are characterized by a single property i e particle s volume we then investigate the extension of the proposed model for solving breakage problems considering two properties of particles the efficiency to estimate the different moments with good accuracy and simple extension for multi variable problems are the key features of the proposed method moreover the mathematical convergence analysis is performed for one dimensional problems all mathematical findings and numerical results are validated over several test problems for numerical validation we propose the extension of bourgade filbet 2008 math comput 77 851 882 doi 10 1090 s0025 5718 07 02054 6 model for solving two dimensional pure breakage problems in this aspect numerical treatment of the two dimensional binary breakage models using finite volume methods can be treated to be the first instance in the literature

discrete order preserving semigroups and stability for periodic parabolic differential equations on etudie la stabilite globale des solutions des equations paraboliques dans une forme non auto adjointe avec des coefficients periodiques dans le temps la structure mathematique est celle des semigroupes preservant l ordre a temps discret s n n e n sur un reseau de banach

convergence to periodic solutions in periodic quasimonotone reaction diffusion systems abstract the author studies the periodic time dependent quasimonotone reaction diffusion systems u i t d i u i f i t x u 1 u n t 0 x u i n i u i 0 t 0 x u i x 0 u 0 i x x formula i 1 2 n in a proper banach space satisfying i fi uj 0 for all 1 i j n ii f t x u is periodic in t of period 0 and iii fi t x u fi t x u for all 0 1 and i 1 2 n it is proved that every solution of such a system converges to a periodic solution the same result also holds if we replace iii by iii f t x u is analytic and every periodic solution is liapounov stable

an abstract theorem in nonlinear analysis and two applications abstract we prove abstract multiplicity theorems for a class of nonlinear equations on the hilbert space l 2 then we use these theorems to deduce new results for two different types of nonlinear boundary value problems

the influence of boundary data on the number of solutions of boundary value problems with jumping nonlinearities this paper contains results concerning the number of solutions as a function of the boundary data for boundary value problems with jumping nonlinearities an example seems to indicate that boundary data has a different influence on this number than does forcing data through approximating techniques this example leads to lower bounds on solution numbers for the more general case

a bounded mountain pass lemma without the ps condition and applications we present a version of the mountain pass lemma which does not require the ps condition we apply this version to problems where the ps condition is not satisfied

characterizations of evenly convex sets and evenly quasiconvex functions the aim of this paper is to present a geometric characterization of even convexity in separable banach spaces which is not expressed in terms of dual functionals or separation theorems as an application an analytic equivalent definition for the class of evenly quasiconvex functions is derived

on the multiplicity of the solution set of some nonlinear boundary value problems ii on considere le probleme non lineaire lu f u s 1 h dans u 0 sur soit h l 2 f est de classe c et que f 1 et n f n 1 n 1 alors il existe s 0 tel que pour tout s s 0 l equation a au moins 2 solutions si n est impair et 3 solutions si n est pair

on linear systems containing strict inequalities this paper deals with systems of an arbitrary possibly infinite number of both weak and strict linear inequalities we analyze the existence of solutions for such kind of systems and show that the large class of convex sets which admit this kind of linear representations i e the so called evenly convex sets enjoys most of the well known properties of the subclass of the closed convex sets we also show that it is possible to obtain geometrical information on these sets from a given linear representation finally we discuss the theory and methods for those linear optimization problems which contain strict inequalities as constraints

homology of saddle point reduction and applications to resonant elliptic systems abstract in the setting of saddle point reduction we prove that the critical groups of the original functional and the reduced functional are isomorphic as application we obtain two nontrivial solutions for elliptic gradient systems which may be resonant both at the origin and at infinity the difficulty that the variational functional does not satisfy the palais smale condition is overcame by taking advantage of saddle point reduction our abstract results on critical groups are crucial

a finite element method for computing the bifurcation function for semilinear elliptic bvps abstract the method of alternative problems can be used to show that a semilinear elliptic boundary value problem lu g x u 0 with gu x u bounded below is equivalent to a finite dimensional problem f c 0 r d c r d in the sense that their solution sets which are not necessarily singletons are in a one to one correspondence this correspondence is based on a map from low frequency to high frequency fourier components of solutions a numerical method is presented for approximating and hence also solutions of the bvp the method uses finite element approximations and avoids the use of eigenfunction expansions existence uniqueness and error estimates for the approximations of and solutions u are derived

existence and stability of time periodic solutions in a model for spherical flames with time periodic heat losses the problem under investigation is the study of the effect of periodicity when time periodic heat losses are added in a model for spherical flames introduced by g joulin in the present context the flame either quenches in finite or infinite time or its radius converges to an upper stable time periodic solution or to a lower unstable time periodic solution

a reaction diffusion system with fast reversible reaction abstract we consider a reaction diffusion system which models a fast reversible reaction between two mobile reactants and prove convergence of the solutions as the reaction rate tends to infinity where the limiting problem is given by a diffusion equation with nonlinear diffusion since the rate function has no sign the usual methods to obtain a priori estimates in the case of irreversible reactions do not apply we deduce instead a priori estimates from computations based on lyapunov function techniques

phase translation group actions on strongly monotone skew product semiflows we establish a convergence property for pseudo bounded forward orbits of strongly monotone skew product semiflows with invariant phasetranslation group actions the results are then applied to obtain global convergence of certain chemical reaction networks whose associated systems in reaction coordinates are monotone as well as the dynamics of certain reactiondiffusion systems in time recurrent structure including periodicity almost periodicity and almost automorphy

remarks on multiple solutions for elliptic resonant problems we obtain four nontrivial solutions for an elliptic resonant problem via morse theory and lyapunov schmidt reduction method our result improves some recent works

a duality approach to minimax results for quasi saddle functions in finite dimensions in this paper we show how saddle point theorems for a quasiconvex quasiconcave function can be derived from duality theory a symmetric duality framework that provides the machinery for deriving saddle point theorems is presented generating the theorems via the framework provides a deeper understanding of assumptions employed in existing theorems which do not utilize duality theory

asymptotic behavior of strongly monotone time periodic dynamical processes with symmetry given a strongly monotone discrete time dynamical system tn x x n z in an open and order convex subset x of a separable strongly ordered banach space v and a compact connected metrizable group g whose action on x is monotone and commutes with t we prove under some reasonable additional hypotheses that the limit set x of every stable point x x consists of symmetric points only i e g w w for all w x and g g moreover the set of all unstable points is contained in a union of at most countably many lipschitz manifolds of codimension one in v where each manifold is invariant under t and the action of g this result is applied to the time periodic spatially independent irreducible cooperative system of n reaction diffusion equations u t d t u f t u for t x r1 rn with spatially periodic boundary conditions in rn and with an initial distribution u0 which is continuous and satisfies the boundary conditions if u0 is stable then u0 contains spatially constant functions only and the dynamics on u0 is given by the irreducible cooperative system of n odes dudt f t u for t r1 here t is the poincare map if n 1 then u0 is a single fixed point of t if n 2 then v0 is a single fixed point of t for each v0 u0

convergence to equilibrium on invariant d hypersurfaces for strongly increasing discrete time semigroups abstract convergence to equilibrium for every positive semi orbit of strongly increasing discrete time semigroups on strongly ordered spaces is proved the domain of the semigroup is assumed to be slightly more general than a closed order interval in a strongly ordered banach space which is continuously imbedded into a banach lattice the semigroup is assumed to be order compact and every positive semi orbit is assumed to be order bounded the crucial hypothesis is the ljapunov stability of all equilibria it is also proved that the set of equilibria is a simply ordered arc the key tools are invariant d hypersurfaces

conjugacy in quasi convex programming this paper develops a symmetric conjugate relation for quasi convex functions the concept of an evenly quasi convex function is introduced and it is shown that this is the required property for a duality framework in quasi convex programming

asymptotic behaviour of comparable skew product semiflows with applications the almost 1 cover lifting property of omega limit sets is established for nonmonotone skew product semiflows which are comparable to uniformly stable eventually strongly monotone skew product semiflows these results are then applied to study the asymptotic behavior of solutions to the nonmonotone comparable systems of odes reaction diffusion systems differential systems with time delays and semilinear parabolic equations

remarks and generalizations related to a recent multiplicity result of a lazer and p mckenna we will show here that this result has a natural generalization to the case that u 5 ai to state the result we consider the model problem lu au autel 2 where 0 0 and set t 0 we have a nonlinear eigenvalue problem lu yu au 4 the following proposition is known cf fueik 3 dancer 2 and also lo where the result appears in the formulation given below

a mountain pass method for the numerical solution of semilinear wave equations it is well known that periodic solutions of semilinear wave equations can be obtained as critical points of related functionals in the situation that we studied there is usually an obvious solution obtained as a solution of linear problem we formulate a dual variational problem in such a way that the obvious solution is a local minimum we then find additional non obvious solutions via a numerical mountain pass algorithm based on the theorems of ambrosetti rabinowitz and ekeland numerical results are presented

development and convergence analysis of a finite volume scheme for solving breakage equation in this paper we develop a new discretization method based on a finite volume approach for solving the breakage population balance equation the scheme is designed to conserve the total mass of the system and predict the total number of particles as well as the complete particle size distribution very accurately the new method is computationally very efficient easy to code and robust to apply on uniform and nonuniform meshes development of the method is completed by providing a detailed mathematical analysis that includes consistency and convergence of the numerical solution it is proved that the scheme is second order convergent independently of the type of mesh moreover numerical results are compared against several test cases including analytically tractable and practically oriented problems it is found that the new method predicts the complete particle size distribution and its moments with high accuracy the mathematical results of convergence analysis are also validated numerically

convergence for pseudo monotone semiflows on product ordered topological spaces in this paper we consider a class of pseudo monotone semiflows which only enjoy some weak monotonicity properties and are defined on product ordered topological spaces under certain conditions several convergence principles are established for each precompact orbit of such a class of semiflows to tend to an equilibrium which improve and extend some corresponding results already known some applications to delay differential equations are presented

approximation to a fokker planck equation for the brownian motor an approximate method is proposed and numerically confirmed for a time dependent fokker planck equation fpe modeling the brownian motor the situation addressed in this paper is that the potential is spatially asymmetric and multiplicatively modulated the approximate solution is composed of sturm liouville eigenfunctions while some time independent partial differential equations and those perturbed around them have been known to be reduced to ordinary differential equations with a few degrees of freedom the time dependent fpe dealt with in this paper is also found to be reduced to an ordinary differential equation

non uniformly asymptotically linear p laplacian problems abstract we relax conditions on uniform convergences of f x s s p 2 s which are essential in many results on multiplicity for asymptotically linear p laplacian problems

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

even convexity subdifferentiability and γ regularization in general topological vector spaces abstract in this paper we provide new results on even convexity and extend some others to the framework of general topological vector spaces we first present a characterization of the even convexity of an extended real valued function at a point we then establish the links between even convexity and subdifferentiability and the regularization of a given function consequently we derive a sufficient condition for strong duality fulfillment in convex optimization problems

stabilization of solutions for a class of degenerate equations in divergence form in one space dimension abstract by extending the concept of the liapunov functional and an idea due to dafermos we establish an invariance principle for a class of not necessarily strongly monotone systems this principle is then applied to continuous contraction strongly monotone systems on a hubert space and to a class of l 1 contraction monotone semigroups generated by degenerate equations in divergence form in one space dimension

extremal equilibria for monotone semigroups in ordered spaces with application to evolutionary equations abstract we consider monotone semigroups in ordered spaces and give general results concerning the existence of extremal equilibria and global attractors we then show some applications of the abstract scheme to various evolutionary problems from odes and retarded functional differential equations to parabolic and hyperbolic pdes in particular we exhibit the dynamical properties of semigroups defined by semilinear parabolic equations in r n with nonlinearities depending on the gradient of the solution we consider as well systems of reaction diffusion equations in r n and provide some results concerning extremal equilibria of the semigroups corresponding to damped wave problems in bounded domains or in r n we further discuss some nonlocal and quasilinear problems as well as the fourth order cahn hilliard equation

multiplicity result for semilinear dissipative hyperbolic equations let zq z r and r be the set of all positive integers integers nonnegative reals and reals respectively and let v r n g 1 be a bounded domain with smooth boundary v which is assumed to be of class c 2 let q s 0 2p v and l q be the space of measurable lebesgue square integrable real valued functions on q with usual inner product 2 5 5 and corresponding norm 2 1 1 by h v we mean the completion of c v with respect to the norm 0 0 5 5 defined by 1

multiplicity results for a semilinear boundary value problem with the nonlinearity crossing higher eigenvalues on etudie le probleme aux valeurs limites au g u h x u 0 ou a est un operateur differentiel lineaire auto adjoint uniformement elliptique d ordre 2

on multiple solutions of a nonlinear neumann problem abstract lower bounds on the number of solutions to a certain class of nonlinear neumann boundary value problems are obtained as a function of boundary data and of the parameters involved with the nonlinear term

on the number of solutions of an elliptic boundary value problem with jumping nonlinearity soit un domaine borne de r n n 2 a frontiere lisse on considere la determination du nombre de solutions du probleme aux valeurs limites u f u h h dans u 0 sur quand varie

multiple solutions for some semilinear elliptic equations on donne des resultats sur le nombre des solutions du probleme de dirichlet pour des equations elliptiques semilineaires

existence of nontrivial solutions of semilinear elliptic equations soit cr n un domaine borne a frontiere lisse et g r r une application continue telle que g 0 0 on etudie l existence des solutions non triviales du probleme aux valeurs limites de la forme u g u dans u 0

multiplicity results for a nonlinear dirichlet problem on donne des resultats de multiplicite pour des problemes elliptiques a non linearites de saut on considere le cas dans lequel seule une valeur propre du probleme lineaire est sautee et est simple

a convex like duality scheme for quasi convex programs this paper describes a symmetric duality relation for quasi convex programs we are able to strengthen previous results and to define necessary and sufficient conditions for the absence of duality gap in the present scheme one can generate quasi convex quasi concave lagrangians and discuss the correspondence between saddle points of the lagrangians and the solutions to the dual and primal programs the present scheme is very similar to rockafellar s scheme for convex programs and in this sense it may be viewed as a unified approach several examples are also given

existence and uniqueness of steady state solution to a singular coagulation fragmentation equation abstract in this article we prove the existence of an equilibrium solution to the coagulation fragmentation equation with i a singular coagulation kernel in the form k x y 1 x y x y where 0 1 2 and 0 1 and ii a fragmentation kernel in the form f x y b 0 b x y m where b 0 0 and b m 0 importantly in the entire study the detailed balance condition is not assumed it is shown that the equilibrium solution of the problem under consideration is unique in the space of all continuous functions on 0 the proposed results are demonstrated by a numerical illustration

the study of nonlinear flexings in a floating beam by variational methods abstract the equation of a floating beam utt uxxxx bu c with free end boundary conditions is studied using the variational methods we show the existence of at least one nontrivial solution which is of the mountain pass type also considered is the beam with one end clamped and the other end free in this case there exist at least two nontrivial solutions the numerical results show the presence of both small and large amplitude flexings moreover they persist in the presence of small damping and arise as solutions of an initial value problem thereby suggesting that some of these solutions have local asymptotic stability properties