Existence Theorems Of Solutions Research Articles

Improvement of an Estimate of the Global Existence Theorem for Solutions of the Bogoliubov Equations

For a one-dimensional system of particles interacting like elastic balls, we improve an estimate of the existence theorem for the global solution of the Cauchy problem for the Bogoliubov equations with initial data from the space of sequences of measurable functions.

Existence of solutions on weak vector equilibrium problems

Weak vector equilibrium problems with bi-variable mappings from product space of two bounded complete locally convex Hausdorff topological vector spaces to another topological vector space are studied. The existence theorems of solutions are proved by the FKKM fixed point theorem. Viscosity principle of vector equilibrium problems is dealt with. The relations between solutions of the vector equilibrium problem and those of its perturbation problem are presented.

Systems of Simultaneous Generalized Vector Quasiequilibrium Problems and their Applications

In this paper, we introduce systems of simultaneous generalized vector equilibrium problems and prove the existence of their solutions. As application of our results, we derive the existence theorems for solutions of systems of vector saddle–point problems. Consequently, we prove the existence of a solution of systems of generalized minimax inequalities. Further application of our results is also given to establish the existence of a solution of a Debreu-type equilibrium problem for vector-valued functions.

EQUILIBRIUM PROBLEMS WITH LOWER AND UPPER BOUNDS IN TOPOLOGICAL SPACES

By employing a fixed point theorem due to Ding, Park and Jung, some existence theorems of solutions for equilibrium problems with lower and upper bounds are proved in noncompact topological spaces. These results further answer the open problem raised by Isac, Sehgal and Singh under much weaker assumptions.

On the existence of solutions to generalized vector variational-like inequalities

In this paper, we consider a vector version of generalized Minty's lemma and obtain existence theorems of solutions for two kinds of vector variational-like inequalities.

Vector [formula omitted]-implicit complementarity problems in Banach spaces

In this work, a new class of vector F -implicit complementarity problems and vector F -implicit variational inequality problems are introduced and studied, and the equivalence between of them is presented under certain assumptions in Banach spaces. We also derive some new existence theorems of solutions for the vector F -implicit complementarity problems and the vector F -implicit variational inequality problems by using the FKKM theorem under some suitable assumptions without monotonicity.

Maximal Element Theorems with Applications to Generalized Games and Systems of Generalized Vector Quasi-Equilibrium Problems in G-Convex Spaces

By applying the maximal element theorems on product of G-convex spaces due to the first author, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in G-convex spaces. As applications, some existence theorems of solutions for the system of generalized vector quasiequilibrium problem are established in noncompact product of G-convex spaces. Our results improve and generalize some recent results in the literature to product of G-convex spaces.

Fixed points for weakly inward mappings in Banach spaces

S. Hu and Y. Sun [S. Hu, Y. Sun, Fixed point index for weakly inward mappings, J. Math. Anal. Appl. 172 (1993) 266–273] defined the fixed point index for weakly inward mappings, investigated its properties and studied the fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we continue to investigate boundary conditions, under which the fixed point index for the completely continuous and weakly inward mapping, denoted by i ( A , Ω , P ) , is equal to 1 or 0. Correspondingly, we can obtain some new fixed point theorems of the completely continuous and weakly inward mappings and existence theorems of solutions for the equations A x = μ x , which extend many famous theorems such as Leray–Schauder's theorem, Rothe's two theorems, Krasnoselskii's theorem, Altman's theorem, Petryshyn's theorem, etc., to the case of weakly inward mappings. In addition, our conclusions and methods are different from the ones in many recent works.

Implicit vector equilibrium problems via nonlinear scalarisation

The purpose of this paper is to introduce a nonlinear scalarisation function for solving a class of implicit vector equilibrium problems. We prove a scalarisation lemma to show the relation between the implicit vector equilibrium problem and the nonlinear scalarisation function. Then we derive some new existence theorems for solutions of implicit vector equilibrium problems, using the scalarisation lemma and the FKKM theorem.

Existence theorems for solutions of variational inequalities

The existence of nonzero solutions for a class of generalized variational inequalities is studied by fixed point index approach for multi-valued mappings in finite dimensional spaces and reflexive Banach spaces.

Perfect bases for differential equations

We present a method for the construction of solutions of certain systems of partial differential equations with polynomial and power series coefficients. For this purpose we introduce the concept of perfect differential operators. Within this framework we formulate division theorems for polynomials and power series. They in turn yield existence theorems for solutions of systems of linear partial differential equations and algorithms to explicitly construct solutions.

Generalized vector quasi-equilibrium problems in locally G-convex spaces

Some classes of generalized vector quasi-equilibrium problems (in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems, generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.

An Existence Theorem of Solutions for Degenerate Semilinear Elliptic Equations

An Existence Theorem of Solutions for Degenerate Semilinear Elliptic Equations

Theoretical analysis of a model of the thermal boundary layer with drag

For solutions of a system of degenerate quasilinear parabolic equations we prove some interior Schauder estimates and use them to establish an existence theorem for solutions of the problem of extending the thermal boundary layer of a compressible fluid in a magnetic field.

Weak linear bilevel programming problems: existence of solutions via a penalty method

We are concerned with a class of weak linear bilevel programs with nonunique lower level solutions. For such problems, we give via an exact penalty method an existence theorem of solutions. Then, we propose an algorithm.

Applications of W. A. Kirk's fixed-point theorem to generalized nonlinear variational-like inequalities in reflexive Banach spaces

We introduce and study a new class of generalized nonlinear variational-like inequalities, which includes these variational inequalities and variational-like inequalities due to Bose, Cubiotti, Dien, Ding, Ding and Tarafdar, Noor, Parida, Sahoo, and Kumar, and Yao, and others as special cases. By applying Kirk's fixed-point theorem and Ding-Tan minimax inequality, we establish the existence theorems of solutions for the generalized nonlinear variational-like inequalities in reflexive Banach spaces.

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.

Three Point Boundary Value Problems on Time Scales

This work formulates existence theorems for solutions to three-point boundary value problems on time scales. The ideas are based on a relationship between the three point boundary conditions, lower and upper solutions and topological degree theory.

F-Implicit Complementarity Problems in Banach Spaces

The F-implicit complementarity problem (F-ICP) and F-implicit variational inequality problem (F-IVIP) are introduced and studied. The equivalence between (F-ICP) and (F-IVIP) is presented under certain assumptions. Furthermore, we derive some new existence theorems of solutions for (F-ICP) and (F-IVIP) by using the Fan–Knaster–Kuratowski–Mazurkiewicz Math. Ann. 142 (1961), 305–310] and Lin's Bull. Austral. Math. Soc. 34 (1986), 107–117] under some suitable assumptions without the monotonicity.

Multi-valued quasi variational inclusions in Banach spaces

The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces. By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established. The results generalize, improve and unify a number of Noor's and others' recent results.