Existence Results Of Solutions Research Articles

Solvability for a class of fractional [formula omitted]-point boundary value problem at resonance

In this paper, the following fractional ordinary differential equation boundary value problem: D 0 + α u ( t ) = f ( t , u ( t ) , D 0 + α − 1 u ( t ) ) + e ( t ) , 0 < t < 1 , I 0 + 2 − α u ( t ) ∣ t = 0 = 0 , u ( 1 ) = ∑ i = 1 m − 2 β i u ( η i ) , is considered, where 1 < α ≤ 2 is a real number, D 0 + α and I 0 + α are the standard Riemann–Liouville differentiation and integration, and f : [ 0 , 1 ] × R 2 → R is continuous and e ∈ L 1 [ 0 , 1 ] , and β i ∈ R , i = 1 , 2 , ⋯ , m − 2 , 0 < η 1 < η 2 < ⋯ < η m − 2 < 1 are given constants such that ∑ i = 1 m − 2 β i η i α − 1 = 1 . By using the coincidence degree theory, some existence results of solutions can be established.

Asymptotic behaviour of solutions of nondivergence type semilinear elliptic equations in conical domains I

We study a special class of solutions to semilinear elliptic equations in conical domains. We prove that under some initial assumption on the solution it is asymptotically close to a linear combination of special solutions of the corresponding homogeneous equation. We also give the existence result for solutions with asymptotics of this type.

Existence of Solutions to Anti-Periodic Boundary Value Problem for Nonlinear Fractional Differential Equations with Impulses

This paper discusses the existence of solutions to antiperiodic boundary value problem for nonlinear impulsive fractional differential equations. By using Banach fixed point theorem, Schaefer fixed point theorem, and nonlinear alternative of Leray-Schauder type theorem, some existence results of solutions are obtained. An example is given to illustrate the main result.

On a Nonlinear Integral Equation with Contractive Perturbation

We get an existence result for solutions to a nonlinear integral equation with contractive perturbation by means of Krasnoselskii's fixed point theorem and especially the theory of measure of weak noncompactness.

Existence and Stability of Solutions for Implicit Multivalued Vector Equilibrium Problems

A class of implicit multivalued vector equilibrium problems is studied. By using the generalized Fan-Browder fixed point theorem, some existence results of solutions for the implicit multivalued vector equilibrium problems are obtained under some suitable assumptions. Moreover, a stability result of solutions for the implicit multivalued vector equilibrium problems is derived. These results extend and unify some recent results for implicit vector equilibrium problems, multivalued vector variational inequality problems, and vector variational inequality problems.

Global compactness results for quasilinear elliptic problems with combined critical Sobolev–Hardy terms

In this paper, we study the global compactness results for quasilinear elliptic problems involving combined critical Sobolev–Hardy terms on the whole space and a bounded smooth domain, respectively. That is, we give the complete descriptions for the Palais–Smale (PS) sequences of the corresponding energy functionals. By using these descriptions, the existence results of solutions are also obtained.

Vector equilibrium problems on unbounded sets

We consider a general vector equilibrium problem in a reflexive Banach space setting and propose a new coercivity condition for the case of unbounded sets. This condition enables us to obtain new existence results of solutions for vector equilibrium problems. We specialize these results for scalar equilibrium problems and vector variational inequalities.

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

In this paper, we discuss the existence of solutions for a three-point boundary value problem of fractional differential equations. Some uniqueness and existence results of solutions are established. Our results are based on the coincidence degree theory.

Remarks on the 2-Dimensional Lp-Minkowski Problem

Abstract Positive periodic solutions of the equation ẍ + x = g(t)xp-1 are considered with continuous and T-periodic g. Some existence results of solutions are obtained by variational method.

Degree theory for a generalized set-valued variational inequality with an application in Banach spaces

In this paper, a degree theory for a generalized set-valued variational inequality is built in a Banach space. As an application, an existence result of solutions for the generalized set-valued variational inequality is given under some suitable conditions.

Generalized Bi-Quasivariational Inequalities for Quasi-Pseudomonotone Type II Operators on Noncompact Sets

We prove some existence results of solutions for a new class of generalized bi-quasivariational inequalities (GBQVI) for quasi-pseudomonotone type II and strongly quasi-pseudomonotone type II operators defined on noncompact sets in locally convex Hausdorff topological vector spaces. To obtain these results on GBQVI for quasi-pseudomonotone type II and strongly quasi-pseudomonotone type II operators, we use Chowdhury and Tan's generalized version (1996) of Ky Fan's minimax inequality (1972) as the main tool.

On variational methods to a generalized Emden–Fowler equation

In the present paper, the variational principle to the boundary value problems for a generalized Emden-Fowler equation is given and some existence results of solutions are obtained by using the critical point theory.

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

The existence result for the system of generalized vector quasi-variational-like inequalities

In this paper, we introduce the system of generalized vector quasi-variational-like inequalities, and establish the existence result of its solutions. As a special case, we also derive the existence result of solutions for the generalized vector quasi-variational-like inequality.

SYSTEMS OF GENERALIZED VECTOR QUASI-VARIATIONAL INCLUSION PROBLEMS AND APPLICATION TO MATHEMATICAL

In this paper, we introduce and study some new systems of generalized vector quasi-variational inclusion problems involving condensing mappings in locally $FC$-uniform spaces. These systems contain many known systems of generalized vector quasi-variational inclusion problems, systems of generalized vector quasi-equilibrium problems and systems of vector quasi-optimization problems as special cases. By applying an existence theorem of maximal elements of a family of set-valued mappings involving condensing mapping due to author, we prove some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems. As applications, some existence results of solutions of the mathematical programs with systems of generalized vector quasi-variational inclusion constraints are established in noncompact locally $FC$-uniform

On the coupling between a Navier–Stokes equation and a total energy equation in spatial dimension [formula omitted

We consider a class of nonlinear evolution systems, namely the Rayleigh–Benard equations. This system arises from the coupling between a Navier–Stokes equation for the velocity and the pressure and a total energy equation in spatial dimension N = 3 . We give a few existence results of solutions under suitable conditions in the right-hand side of the momentum equation, the forcing term depending on the temperature. To this end, we begin to solve an approximated problem, namely the Boussinesq system resulting from the Rayleigh–Benard equations through a fixed-point argument. Next, by a linear combination, we construct a new equivalent system. Finally, we give a priori estimates and compactness results before passing to the limit in the equivalent system.

A symmetrization of the relativistic Euler equations with several spatial variables

We consider the Euler equations governing relativistic compressible fluids evolving in the Minkowski spacetime with several spatial variables. We propose a new symmetrization which makes sense for solutions containing vacuum states and, for instance, applies to the case of compactly supported solutions which are important to model star dynamics. Then, relying on these symmetrization and assuming that the velocity does not exceed some threshold and remains bounded away from the light speed, we deduce a local-in-time existence result for solutions containing vacuum states. We also observe that the support of compactly supported solutions does not expand as time evolves.

Existence of Solutions to the System of Generalized Implicit Vector Quasivariational Inequality Problems

We study the system of generalized implicit vector quasivariational inequality problems and prove a new existence result of its solutions by Kakutani-Fan-Glicksberg's fixed points theorem. As a special case, we also derive a new existence result of solutions to the generalized implicit vector quasivariational inequality problems.

Existence of Nontrivial Solution for a Nonlocal Elliptic Equation with Nonlinear Boundary Condition

In this paper, we establish two different existence results of solutions for a nonlocal elliptic equations with nonlinear boundary condition. The first one is based on Galerkin method, and gives a priori estimate. The second one is based on Mountain Pass Lemma.

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type I operators on compact sets

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type I operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type I operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.