the existence of multiple equilibrium points in a global attractor for some p laplacian equation abstract in this paper we are mainly concerned with some properties of the global attractor for some p laplacian equation with a lyapunov function in a banach space under some suitable assumptions we prove the existence of multiple equilibrium points in a global attractor for some p laplacian equation

infinitely many non negative solutions for a dirichlet problem involving p x laplacian abstract in this paper we consider a dirichlet problem involving the p x laplacian of the type div u p x 2 u f x u in u 0 on we prove the existence of infinitely many non negative solutions of the problem by applying a general variational principle due to b ricceri and the theory of the variable exponent sobolev spaces

three solutions for a dirichlet boundary value problem involving the p laplacian abstract in this paper we prove the existence of at least three weak solutions for the problem p u f x u a x u p 2 u in u 0 on our main tool is a recent three critical points theorem of b ricceri on a three critical points theorem arch math basel 75 2000 220 226

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

a more powerful method for triangularizing input output matrices and the similarity of production structures studies in the production structure of any national economy as revealed in its inputoutput table have been closely related to the question of the interindustrial dependence or hierarchical structures of productive sectors leading from primary to final production in particular the notion of hierarchy provides a useful tool when one wants to draw inferences on the structural change or international difference of industrial structures the standard technique for studying this notion is to triangularize the input output table by interchanging sectors in order to maximize the entries below the main diagonal in a perfect triangularized table the entries above the main diagonal should be zero for example such a strong one way interdependence relation as cotton textiles clothing can easily establish the hierarchy due to the existence of circular relations like coal steel mining equipment coal it is not possible to triangularize the input output table perfectly this paper extends and revises the previous triangulation method which is based on a permutation theorem deriving from the interchange of adjoining two industrial groups into that among three industrial groups theorem 2 the new algorithm based on theorem 2 is demonstrated by actually computing the suboptimal orderings for the four input output tables for such more developed countries mdc s as the united states italy norway japan and the two tables for such less developed countries ldc s as india and korea the empirical results suggest that sectors can be arranged in a similar hierarchical order among mdc s and ldc s transport equipment machinery apparel leather and products grain mill products and processed foods which link directly to the final demand are recorded as higher order sectors trade transport and services are lower order ones and energy sectors such as electric power coal products coal mining petroleum petroleum products and natural gas are the lowest consequently this paper provides some more evidence in support of the similarity of hierarchical structures of production among these countries

existence of infinitely many solutions for a neumann problem involving the p x laplacian abstract in this paper we consider the neumann problem involving the p x laplacian of the type div u p x 2 u x u p x 2 u f x u g x u in u 0 on we prove the existence of infinitely many solutions of the problem under weaker hypotheses by applying a variational principle due to b ricceri and the theory of the variable exponent sobolev spaces our results are an improvement and generalization of the relative results obtained by b ricceri for the p laplacian case

detection of arbitrarily many solutions for perturbed elliptic problems involving oscillatory terms we propose a direct approach for detecting arbitrarily many solutions for perturbed elliptic problems involving oscillatory terms although the method works in various frameworks we illustrate it on the problem

an algorithm for finding block triangular forms in this paper an algorithm is constructed for finding the block triangular form of a nonnegative matrix the algorithm is based on the zero elements of the left and right perron vectors of the matrix and subsequently certain submatrices the construction of the algorithm is motivated by the empirical results of measuring sectoral interdependencies in the production structure of an economy

a critical point theorem and existence results for a nonlinear boundary value problem in this paper the existence of non zero solutions to a neumann boundary value problem is established multiplicity results are also pointed out the approach is based on a novel critical point theorem

infinitely many solutions for a neumann type differential inclusion problem involving the p x laplacian abstract in this paper we consider a differential inclusion problem involving the p x laplacian of the type div u p x 2 u x u p x 2 u f x u g x u in u 0 on we prove the existence of infinitely many solutions of this problem under suitable hypotheses by applying a non smooth ricceri type variational principle and the theory of the variable exponent sobolev spaces

perturbations from symmetric elliptic boundary value problems abstract we study the multiplicity of solutions for the elliptic problem u f x u eg x u in and u 0 on where e is a parameter is a smooth bounded domain in r n f c r f x t is odd with respect to t and g c r under suitable conditions only on f we prove that for any j n there exists ej 0 such that if e ej then the above problem possesses at least j distinct solutions

a momentum construction for circle invariant kahler metrics examples of kahler metrics of constant scalar curvature are relatively scarce over the past two decades several workers in geometry and physics have used symmetry reduction to construct complete kahler metrics of constant scalar curvature by ode methods one fruitful idea the calabi ansatz is to begin with an hermitian line bundle p l h m g m over a kahler manifold and to search for kahler forms p m dd c f t in some disk subbundle where t is the logarithm of the norm function and f is a function of one variable our main technical result theorem a is the calculation of the scalar curvature for an arbitrary kahler metric g arising from the calabi ansatz this suggests geometric hypotheses which we call a constancy to impose upon the base metric g m and hermitian structure h in order that the scalar curvature of g be specified by solving an ode we show that constancy is necessary and sufficient for the calabi ansatz to work in the following sense under the assumption of constancy the disk bundle admits a one parameter family of complete kahler metrics of constant scalar curvature that restrict to g m on the zero section theorems b and d an analogous result holds for the punctured disk bundle theorem c a simple criterion determines when such a metric is einstein conversely in the absence of constancy the calabi ansatz yields at most one metric of constant scalar curvature in either the disk bundle or the punctured disk bundle theorem e many of the metrics constructed here seem to be new including a complete negative einstein kahler metric on the disk subbundle of a stable vector bundle over a riemann surface of genus at least two and a complete scalar flat kahler metric on c 2

remarks on ricceri s variational principle and applications to the p x laplacian equations abstract in this paper we give some remarks on a variational principle of ricceri in the case of sequentially weakly lower semi continuous functionals defined on a reflexive real banach space in particular we introduce the notions of ricceri block and ricceri box which are more convenient in some applications than the weakly connected components using the variational principle of ricceri and a local mountain pass lemma we study the multiplicity of solutions of the p x laplacian equations with neumann dirichlet or no flux boundary condition and under appropriate hypotheses in which the integral functionals need not satisfy the ps condition on the global space we prove that the problem has at least seven solutions

infinitely many solutions for a class of discrete non linear boundary value problems the existence of infinitely many solutions for a discrete non linear dirichlet problem involving the p laplacian under appropriate oscillating behaviours of the non linear term is established the approach is based on the critical point theory

perturbed kirchhoff type neumann problems in orlicz sobolev spaces the aim of this paper is to establish the existence of infinitely many solutions for perturbed kirchhoff type non homogeneous neumann problems involving two parameters to be precise we prove that an appropriate oscillating behaviour of the nonlinear term even under small perturbations ensures the existence of infinitely many solutions our approach is based on recent variational methods for smooth functionals defined on orlicz sobolev spaces

on a nonlinear elliptic eigenvalue problem abstract let n be the number of the solutions of the equation u f u in u 0 on where is a bounded domain in r n n 2 with smooth boundary under suitable conditions on f we proved that n as

minimization on spheres of coercive functionals on w01 2 ω abstract we deal with the minimization on spheres of functionals defined on the space w 0 1 2 we apply the main results to establish a multiplicity theorem for a dirichlet problem involving equations of the type u h x u s 2 u g x u here is the laplacian operator is a real parameter s 1 2 h c is a function which is allowed to be sign changing and g r r r n is a caratheodory function having no growth conditions with respect to the second variable

on the nonlinear schrodinger equation on the poincare ball model abstract in this paper we prove the existence of a sequence of nonnegative weak solutions for the following problem h u u f u in b n u h 1 2 b n where h denotes the laplace beltrami operator on the poincare ball model b n with n 3 of the hyperbolic space h n l 1 b n l b n is a nonnegative and not identically zero radially symmetric potential f is a suitable continuous function and is a positive real parameter the analysis developed in this paper combines a compactness embedding result due to skrzypczak and tintarev 2013 theorem 1 3 and proposition 3 1 some group theoretical arguments on the poincare ball model b n and variational methods for smooth functionals defined on the sobolev space h 1 2 b n associated to the homogeneous hadamard manifold b n

hamiltonian 2 forms in kahler geometry iii extremal metrics and stability this paper concerns the existence and explicit construction of extremal kahler metrics on total spaces of projective bundles which have been studied in many places we present a unified approach motivated by the theory of hamiltonian 2 forms as introduced and studied in previous papers in the series but this paper is largely independent of that theory

extremal kahler metrics on projective bundles over a curve let m p e be the complex manifold underlying the total space of the projectivization of a holomorphic vector bundle e over a compact complex curve of genus 2 building on ideas of fujiki 1992 27 we prove that m admits a kahler metric of constant scalar curvature if and only if e is polystable we also address the more general existence problem of extremal kahler metrics on such bundles and prove that the splitting of e as a direct sum of stable subbundles is necessary and sufficient condition for the existence of extremal kahler metrics in kahler classes sufficiently far from the boundary of the kahler cone the methods used to prove the above results apply to a wider class of manifolds called rigid toric bundles over a semisimple base which are fibrations associated to a principal torus bundle over a product of constant scalar curvature kahler manifolds with fibres isomorphic to a given toric kahler variety we discuss various ramifications of our approach to this class of manifolds

some remarks on a three critical points theorem abstract some remarks on a strict minimax inequality which plays a fundamental role in ricceri s three critical points theorem are presented as a consequence some recent applications of ricceri s theorem to nonlinear boundary value problems are revisited by obtaining more precise conclusions

the kahler geometry of bott manifolds abstract we study the kahler geometry of stage n bott manifolds which can be viewed as n dimensional generalizations of hirzebruch surfaces we show using a simple induction argument and the generalized calabi construction from 3 6 that any stage n bott manifold m n admits an extremal kahler metric we also give necessary conditions for m n to admit a constant scalar curvature kahler metric we obtain more precise results for stage 3 bott manifolds including in particular some interesting relations with c projective geometry and some explicit examples of almost kahler structures to place these results in context we review and develop the topology complex geometry and symplectic geometry of bott manifolds in particular we study the kahler cone the automorphism group and the fano condition we also relate the number of conjugacy classes of maximal tori in the symplectomorphism group to the number of biholomorphism classes compatible with the symplectic structure

existence results for dynamic sturm liouville boundary value problems via variational methods abstract several conditions ensuring existence of solutions of a dynamic sturm liouville boundary value problem are derived variational methods are utilized in the proofs an example illustrating the main results is given

arbitrarily many solutions for a perturbed p x laplacian equation involving oscillatory terms this paper deals with a perturbed p x laplacian equation involving oscillatory terms div u p x email protected u u p x 2u q x f u email protected u email protected r n u 0 u x 0as x by using variational methods and the non smooth version symmetric criticality principle we establish a the unperturbed problem p 0 has infinitely many distinct solutions b the number of distinct solutions for p e becomes greater and greater whenever e is smaller and smaller our results are a generalization of the case of laplacian from kristaly to the case of p x laplacian

existence and multiplicity of solutions for fourth order boundary value problems with parameters abstract in this paper we study the existence and multiplicity of the solutions for the fourth order boundary value problem bvp u 4 t u t u t f t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r is continuous r and r are parameters by means of the idea of the decomposition of operators shown by chen w y chen a decomposition problem for operators xuebao of dongbei renmin university 1 1957 95 98 see also m krasnosel skii topological methods in the theory of nonlinear integral equations gostehizdat moscow 1956 and the critical point theory we obtain that if the pair is on the curve 2 4 satisfying 2 2 then the above bvp has at least one two three and infinitely many solutions for being in different interval respectively

central kahler metrics with non constant central curvature the central curvature of a riemannian metric is the determinant of its ricci endomorphism while the scalar curvature is its trace a kahler metric is called central if the gradient of its central curvature is a holornorphic vector field such metrics may be viewed as analogs of the extremal kahler metrics defined by calabi in this work central metrics of non constant central curvature are constructed on various ruled surfaces most notably the first hirzebruch surface this is achieved via the momentum construction of hwang and singer a variant of an ansatz employed by calabi 1979 and by koiso and sakane 1986 non existence real analyticity and positivity properties of central metrics arising in this ansatz are also established

multiple solutions for two nonlinear problems involving the p laplacian abstract using variational arguments we prove the existence of at least two solutions for two elliptic problems involving the p laplacian dirichlet and neumann boundary conditions will be considered in the two problems where a positive parameter appears

multiple constant sign and nodal solutions for nonlinear elliptic equations with the p laplacian we consider a nonlinear elliptic equation driven by the p laplacian with dirichlet boundary conditions using variational techniques combined with the method of upper lower solutions and suitable truncation arguments we establish the existence of at least five nontrivial solutions two positive two negative and a nodal sign changing solution our framework of analysis incorporates both coercive and p superlinear problems also the result on multiple constant sign solutions incorporates the case of concave convex nonlinearities

perturbation from dirichlet problem involving oscillating nonlinearities in this paper we prove that if the potential f x t 0tf x s ds has a suitable oscillating behavior in any neighborhood of the origin respectively then under very mild conditions on the perturbation term g for every k n there exists bk 0 such that u f x u g x u in u 0on has at least k distinct weak solutions in w01 2 for every r with bk moreover information about the location of such solutions is also given in fact there exists a positive real number 0 which does not depend on such that the w01 2 norm of each of those k solutions is not greater than

existence of solutions for a perturbed dirichlet problem without growth conditions we present some results on the existence and multiplicity of solutions for boundary value problems involving equations of the type u f x u g x u where is the laplacian operator is a real parameter and f g r r rn are two caratheodory functions having no growth conditions with respect to the second variable the approach is variational and mainly based on a critical point theorem by b ricceri

variational elliptic problems which are nonquadratic at infinity p co if n 1 2 then it is well known that the weak solutions u e h 2 of p are the critical points of the c functional j u ulvul dx jcf x u dx where f x s jif x t dt in this variational setting the literature usually distinguishes between two situations for prob lem p the subquadratic situation where the potential f satisfies lim suplsl f x s s2 i c m and the superquadratic situation where f satisfies limlsl m f x s s2 00 the main goal of this paper is to present a unified approach to both situations by means of a condition of nonquadraticity at infinity on f more precisely our hypotheses are as follows

a general variational principle and some of its applications abstract in this paper given a reflexive real banach space x and two sequentially weakly lower semicontinuous functionals on x with strongly continuous and coercive we are mainly interested in the existence of infinitely many local minima of the functional for each sufficiently large r

three solutions for a perturbed dirichlet boundary value problem involving the p laplacian abstract in this paper we study the perturbed dirichlet problem p u a x u p 2 u f x u g x u in u 0 on some existence results of three solutions are obtained by using a three critical points theorem proved by g bonanno 2003 g bonanno some remarks on a three critical points theorem nonlinear anal 54 2003 651 665

on the relationship between two three critical point theorems abstract in this paper we analyze the hypotheses of two theorems which have proven to be useful tools for obtaining the existence of three critical points in nonlinear problems in both cases the hypotheses can be stated in terms of some elementary inequalities involving coercive in a suitable sense sets of affine functions we prove that the two resulting inequalities are in fact equivalent

three solutions for a perturbed dirichlet problem abstract in this paper we prove the existence of at least three distinct solutions to the following perturbed dirichlet problem u f x u g x u in u 0 on where r n is an open bounded set with smooth boundary and r under very mild conditions on g and some assumptions on the behaviour of the potential of f at 0 and our result assures the existence of at least three distinct solutions to the above problem for small enough moreover such solutions belong to a ball of the space w 0 1 2 centered in the origin and with radius not dependent on

radial solutions of dirichlet problems with concave convex nonlinearities abstract we prove the existence of a double infinite sequence of radial solutions for a dirichlet concave convex problem associated with an elliptic equation in a ball of r n we are interested in relaxing the classical positivity condition on the weights by allowing the weights to vanish the idea is to develop a topological method and to use the concept of rotation number the solutions are characterized by their nodal properties

multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods in this paper a coupled system of nonlinear fractional differential equations is considered the existence of at least three distinct weak solutions is obtained by means of the variational methods and the critical point theory due to bonanno and marano in addition an example is presented to illustrate the feasibility and effectiveness of the main results

stability of vector bundles and extremal metrics on donne des exemples de surfaces reglees m qui n ont pas de champs holomorphes vectoriels non triviaux et qui n admettent pas de metrique de kahler extremale dans une classe de kahler specifique donnee

uniform convexity of musielak orlicz sobolev spaces and applications abstract this paper deals with uniform convexity of musielak orlicz sobolev spaces and its applications to variational problems some sufficient conditions and examples for uniform convexity of musielak orlicz sobolev spaces are given some special properties relative to the uniformly convex modular for uniformly convex musielak orlicz sobolev spaces are presented as an application of these abstract results the local minimizers and the mountain pass type critical point of an integral functional with more complicated growth than the p x growth are studied

existence of three solutions for a non homogeneous neumann problem through orlicz sobolev spaces abstract the aim of this paper is to establish a multiplicity result for an eigenvalue non homogeneous neumann problem which involves a nonlinearity fulfilling a nonstandard growth condition precisely a recent critical points result for differentiable functionals is exploited in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three weak solutions in an appropriate orlicz sobolev space

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

three solutions to a perturbed nonlinear discrete dirichlet problem using critical point theory we study the existence of at least three solutions for a perturbed nonlinear dirichlet boundary value problem for difference equations depending on two positive parameters

non differentiable functionals and applications to elliptic problems with discontinuous nonlinearities abstract multiple critical points theorems for non differentiable functionals are established applications both to elliptic variational hemivariational inequalities and eigenvalue problems with discontinuous nonlinearities are then presented

existence of extremal metrics on compact almost homogeneous kahler manifolds with two ends in this note we prove the existence and the uniqueness of extremal metrics in every kahler class of any compact almost homogeneous kahler manifold with two ends by considering the scalar curvature equations those manifolds might not be projective we also prove that there are extremal metrics ini some kahler classes of a completion of the multicanonical line bundle of a kahler einstein manifold of positive ricci curvature

infinitely many solutions for the dirichlet problem involving the p laplacian abstract using a recent variational principle of ricceri we present a result of existence of infinitely many solutions for the dirichlet problem involving the p laplacian