Periodic solutions for some nonautonomous p(t)-Laplacian Hamiltonian systems

In this paper, we deal with the existence of periodic solutions of the p(t)-Laplacian Hamiltonian system . Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.     

Comparison theorems and existence theorems for ordinary differential equations

We are concerned with uniqueness and existence theorems for two point boundary value problems for the nonlinear differential equation Ly = f(x, y), where L is the classical nth order linear differential operator. In proving our results interesting comparison theorems are proven for linear differential equations.     

Hammerstein Integral Equations with Nontrivial Solutions

By means of critical point theory, existence theorems for nontrivial solutions to the Hammerstein equation x = KFx are given, where K is a compact linear integral operator and F is a nonlinear superposition operator. To this end, appropriate conditions on the spectrum of the linear parte are combined with growth and representation conditions on the nonlinear part to ensure the applicability of the mountain — pass lemma. The abstract existence theorems are applied to nonlinear elliptic equations and systems subject to Dirichlet boundary conditions.     

Solutions of system of generalized vector quasi-equilibrium problems in locally G-convex uniform spaces

In this paper we establish a collectively fixed point theorem and an equilibrium existence theorem for generalized games in product locally G-convex uniform spaces. As applications, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are derived in product locally G-convex uniform spaces. These theorems are new and generalize some known results in the literature.     

KKM type theorems and generalized vector equilibrium problems in noncompact FC-spaces

A new KKM type theorem is first proved under noncompact setting of FC-spaces. As applications of the KKM type theorem, we establish some new existence theorems of solutions for generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.     

A unification of the existence theorems of the nonlinear complementarity problem

The nonlinear complementarity problem is the problem of finding a point x in the n-dimensional Euclidean space,R ⁿ , such that x ? 0, f(x) ? 0 and 〈x,f(x)～ = 0, where f is a nonlinear continuous function fromR ⁿ into itself. Many existence theorems for the problem have been established in various ways. The aim of the present paper is to treat them in a unified manner. Eaves's basic theorem of complementarity is generalized, and the generalized theorem is used as a unified framework for several typical existence theorems.     

Lie and Engel theorems for n-tuple lie algebras

We prove some analogs of the Lie and Engel theorems for n-tuple Lie algebras. Furthermore, we establish existence of Cartan subalgebras in the n-tuple Lie algebras.     

Coefficient bounds for biholomorphic mappings which have a parametric representation

The main purpose of this paper is to prove a collection of new fixed point theorems for so-called weakly F-contractive mappings. By analogy, we introduce also a class of strongly F-expansive mappings and we prove fixed point theorems for such mappings. We provide a few examples, which illustrate these results and, as an application, we prove an existence and uniqueness theorem for the generalized Fredholm integral equation of the second kind. Finally, in Appendix A, we apply the Mönch fixed point theorem to prove two results on the existence of approximate fixed points of some continuous mappings.     

Necessary and sufficient conditions for the existence of positive solutions of fourth order multi-point boundary value problems

This paper investigates the existence of positive solutions of singular multi-point boundary value problems of fourth order ordinary differential equation with p-Laplacian. A necessary and sufficient condition for the existence of C²[0,1] positive solution as well as pseudo-C³[0,1] positive solution is given by means of the fixed point theorems on cones.     

Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities

In this paper, we establish some fixed point theorems for a family of multivalued maps under mild conditions. By using our fixed point theorems, we derive some maximal element theorems for a particular family of multivalued maps, namely the Φ-condensing multivalued maps. As applications of our results, we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences. Further applications of our results are also given to minimax inequalities for a family of functions.     

Existence of solutions and existence of optimal solutions. The quasi linear case

By properties of operators of the Brezis type (m), monotone operator theory, and fixed point theorems, the authors prove existence theorems for solutions, and existence theorems for optimal solutions, in problems monitored by nonlinear abstract parabolic type equations. Applications are made to Cauchy-Dirichlet and to Cauchy-Neumann problems, in a cylinder. It is shown that seminormality requirements of previous papers can be dropped. In an alternative approach, controllability results are obtained by a direct application of Kakutani type fixed point theorems.     

Maximal element theorems in product FC-spaces and generalized games

Let I be a finite or infinite index set, X be a topological space and (Yi,{φNi})_i∈I be a family of finitely continuous topological spaces (in short, FC-space). For each i∈I, let be a set-valued mapping. Some existence theorems of maximal elements for the family {Ai}_i∈I are established under noncompact setting of FC-spaces. As applications, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in noncompact FC-spaces. These theorems improve, unify and generalize many important results in recent literature.     

On the existence of ɛ-fixed points

In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ?-Nash equilibria.     

Some fixed-point theorems and minimax inequalities in FC-space

By applying the existence theorem of maximal elements, some new collectively fixed-point theorems for a family of set-valued mappings defined on the product space of noncompact FC-space are proved and some new theorems about minimax inequality involving two functions are given to show the relations of fixed-point theorem and minimax inequality in FC-spaces. These results improve and generalize many important results in the recent literature.     

New systems of generalized quasi-variational inclusions in FC-spaces and applications

In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.     

Periodic solutions for a nonlinear (q,p)-Laplacian dynamical system with impulsive effects

In this paper, some existence theorems are obtained for periodic solutions of a nonlinear (q,p)-Laplacian dynamical system with impulsive effects by using the least action principle and mountain pass theorem.     

A necessary and sufficient condition for 2nth-order singular super-linear m-point boundary value problems

In this paper, we study the existence of positive solutions for singular super-linear m-point boundary value problems of 2nth-order ordinary differential equations. A necessary and sufficient condition for the existence of C2n−2[0,1] positive solutions as well as C2n−1[0,1] positive solutions is given by means of the fixed point theorems on cones.     

High energy solutions and nontrivial solutions for fourth-order elliptic equations

In this paper, we study the existence of nontrivial solutions and infinitely many high energy solutions for a class of nonlinear fourth-order elliptic equations in RN via variational methods. Three main theorems are obtained.     

Periodic solutions for functional-differential equations of mixed type

In this paper we study the existence of ω-periodic solutions for some functional-differential equations of mixed type. Among the main results are the averaging principle and existence theorems for some equations with homogeneous nonlinearities. We use here the coincidence degree theory of Mawhin.     

Existence of positive solutions for the p-Laplacian with p-gradient term

In this paper, we study the existence of positive solutions for the p-Laplacian involving a p-gradient term. Due to the non-variational structure and the fact that the nonlinearity may be critical or supercritical, the variational method is no longer valid. Taking advantage of global C1,α estimates and the Liouville type theorems, we employ the blow-up argument to obtain the a priori estimates on solutions, and finally obtain the existence result based on the Krasnoselskii fixed point theorem.