Existence of positive solutions to n-point nonhomogeneous boundary value problem

In this paper, we are concerned with the existence of positive solutions to a n-point nonhomogeneous boundary value problem. By using the Krasnoselskii's fixed point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of positive solution is established for the n-point nonhomogeneous boundary value problem.     

Nonlinear eigenvalue Neumann problems with discontinuities

In this paper we study nonlinear eigenvalue problems with Neumann boundary conditions and discontinuous terms. First we consider a nonlinear problem involving the p-Laplacian and we prove the existence of a solution for the multivalued approximation of it, then we pass to semilinear problems and we prove the existence of multiple solutions. The approach is based on the critical point theory for nonsmooth locally Lipschitz functionals.     

The directional p-median problem: Definition,complexity, and algorithms

An instance of a p-median problem gives n demand points. The objective is to locate p supply points in order to minimize the total distance of the demand points to their nearest supply point. p-Median is polynomially solvable in one dimension but NP-hard in two or more dimensions, when either the Euclidean or the rectilinear distance measure is used. In this paper, we treat the p-median problem under a new distance measure, the directional rectilinear distance, which requires the assigned supply point for a given demand point to lie above and to the right of it. In a previous work, we showed that the directional p-median problem is polynomially solvable in one dimension; we give here an improved solution through reformulating the problem as a special case of the constrained shortest path problem. We have previously proven that the problem is NP-complete in two or more dimensions; we present here an efficient heuristic to solve it. Compared to the robust Teitz and Bart heuristic, our heuristic enjoys substantial speedup while sacrificing little in terms of solution quality, making it an ideal choice for real-world applications with thousands of demand points.     

Existence of positive solutions for three-point boundary value problems at resonance

With the help of the theorem of a fixed point index for A-proper semilinear operators established by Cremins, we get a existence theorem concerning the existence of positive solution for the second order ordinary differential equation of three-point boundary value problems at resonance.     

Existence results for Stampacchia and Minty type vector variational inequalities

In this article, we consider the general forms of Stampacchia and Minty type vector variational inequalities for bifunctions and establish the existence of their solutions in the setting of topological vector spaces. We extend these vector variational inequalities for set-valued maps and prove the existence of their solutions in the setting of Banach spaces as well as topological vector spaces. We point out that our vector variational inequalities extend and generalize several vector variational inequalities that appeared in the literature. As applications, we establish some existence results for a solution of the vector optimization problem by using Stampacchia and Minty type vector variational inequalities.     

A modified objective function method for solving nonlinear multiobjective fractional programming problems

A new method is used for solving nonlinear multiobjective fractional programming problems having V-invex objective and constraint functions with respect to the same function η. In this approach, an equivalent vector programming problem is constructed by a modification of the objective fractional function in the original nonlinear multiobjective fractional problem. Furthermore, a modified Lagrange function is introduced for a constructed vector optimization problem. By the help of the modified Lagrange function, saddle point results are presented for the original nonlinear fractional programming problem with several ratios. Finally, a Mond-Weir type dual is associated, and weak, strong and converse duality results are established by using the introduced method with a modified function. To obtain these duality results between the original multiobjective fractional programming problem and its original Mond-Weir duals, a modified Mond-Weir vector dual problem with a modified objective function is constructed.     

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.     

On equilibrium problem of abstract economy, generalized quasi-variational inequality, and an optimization problem in locally H-convex spaces

In this paper, the equilibrium existence problem for abstract economies, the existence problem for solution of generalized quasi-variational inequality, and an optimization problem in locally H-convex spaces are researched.     

Nonlinear problems arising in electrostatic actuation in MEMS

In this paper we study the nonlinear problem arising in electrostatic actuation of MEMS. We show that the existence and non-existence of the solution of this problem depend on the value of the physical parameters of the equation. In addition we consider the corresponding initial value problem and we derived the existence of periodic solution, stability of steady states and the ω-limit set.     

Existences theorems of systems of vector quasi-equillibrium problems and mathematical programs with equilibrium constraint

In this paper, we introduce systems of vector quasi-equilibrium problems and prove the existence of their solutions. As applications of our results, we derive the existence theorems for solution of system of vector quasi-saddle point problem, the existences theorems of a solution of system of generalized quasi-minimax inequalities, the mathematical program with equilibrium constraint, semi-infinite and bilevel problems.     

An obstacle problem for nonlinear hemivariational inequalities at resonance

In this paper we examine an obstacle problem for a nonlinear hemivariational inequality at resonance driven by the p-Laplacian. Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz functionals defined on a closed, convex set, we prove two existence theorems. In the second theorem we have a pointwise interpretation of the obstacle problem, assuming in addition that the obstacle is also a kind of lower solution for the nonlinear elliptic differential inclusion.     

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.     

An η-approximation approach to duality in mathematical programming problems involving r-invex functions

An η-approximation approach introduced by Antczak [T. Antczak, A new method of solving nonlinear mathematical programming problems involving r-invex functions, J. Math. Anal. Appl. 311 (2005) 313-323] is used to obtain a solution Mond-Weir dual problems involving r-invex functions. η-Approximated Mond-Weir dual problems are introduced for the η-approximated optimization problem constructed in this method associated with the original nonlinear mathematical programming problem. By the help of η-approximated dual problems various duality results are established for the original mathematical programming problem and its original Mond-Weir duals.     

Asymptotic behavior of Timoshenko beam with dissipative boundary feedback

This paper is concerned with the stabilization problem of Timoshenko beam in the presence of linear dissipative boundary feedback controls. Using C₀-semigroups theory we establish the existence and the uniqueness of solution of the proposed closed loop system. In order to consider the asymptotic behavior of the closed loop system, we first discuss the existence of nonzero solution of a closely related boundary value problem. Then we derive various necessary and sufficient conditions for the system to be asymptotically stable. Finally, we prove the equivalence between the exponential stability and the asymptotic stability for the closed loop system.     

Multiple positive solutions of singular eigenvalue type problems involving the one-dimensional p-Laplacian

We establish a existence result of multiple positive solutions for a singular eigenvalue type problem involving the one-dimensional p-Laplacian. Furthermore, we obtain a nonexistence result of positive solutions by taking advantage of the internal geometric properties related to the problem. Our approach is based on the fixed point index theory and the fixed point theorem in cones.     

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.     

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.     

Higher-order Lidstone boundary value problems for elliptic partial differential equations

The aim of this paper is to show the existence and uniqueness of a solution for a class of 2nth-order elliptic Lidstone boundary value problems where the nonlinear functions depend on the higher-order derivatives. Sufficient conditions are given for the existence and uniqueness of a solution. It is also shown that there exist two sequences which converge monotonically from above and below, respectively, to the unique solution. The approach to the problem is by the method of upper and lower solutions together with monotone iterative technique for nonquasimonotone functions. All the results are directly applicable to 2nth-order two-point Lidstone boundary value problems.     

Existence and multiplicity of solutions to 2mth-order ordinary differential equations

In this paper, the existence and multiplicity of solutions are obtained for the 2mth-order ordinary differential equation two-point boundary value problems u(2(m−i))(t)=f(t,u(t)) for all t∈[0,1] subject to Dirichlet, Neumann, mixed and periodic boundary value conditions, respectively, where f is continuous, ai∈R for all i=1,2,…,m. Since these four boundary value problems have some common properties and they can be transformed into the integral equation of form , we firstly deal with this nonlinear integral equation. By using the strongly monotone operator principle and the critical point theory, we establish some conditions on f which are able to guarantee that the integral equation has a unique solution, at least one nonzero solution, and infinitely many solutions. Furthermore, we apply the abstract results on the integral equation to the above four 2mth-order two-point boundary problems and successfully resolve the existence and multiplicity of their solutions.     

Duality in ε-variational inequality problems

In this paper a general analysis of duality for an extended ε-variational inequality problem based on the notions of ε-convexity and ε-conjugacy is performed. Optimal solutions of both the primal and dual problems are also related to the saddle point of an associated Lagrangian. Gap functions for these problems are proposed. An existence theorem for the extended ε-variational inequality is also established by means of the KKM lemma.