In this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear, infinite dimensional optimal control problems. The parameter appears in all the data of the problem, including the subdifferential operator. First we establish several continuity results for the solution multifunction of the subdifferential inclusio...

* Correspondence: J.W. [email protected] School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, PR China Full list of author information is available at the end of the article Abstract In order to unify some variational inequality problems, in this paper, a new system of generalized quasivariational inclusion (for short, (SGQVI)) is introduced. By using Banach contraction pr...

The purpose of this work, we present a new iterative algorithm for finding a common of the set of solutions of a mixed equilibrium problem, the set of a variational inclusion and the set of fixed point of nonexpansive mapping in a real Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. The results p...

In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...

ABSTRACT. This paper is devoted to optimal control problem of stochastic switching systems. Dynamics of this processes governed by stochastic differential equations with control terms in the drift and diffusion coefficients. Necessary conditions for optimality of described systems with the restrictions in each interval are obtained. The constraints on the transitions are described by the set of...

Abstract In this paper, we introduce a regularization method for solving the variational inclusion problem of sum two monotone operators in real Hilbert spaces. We suggest and analyze under some mild appropriate conditions imposed on parameters, which allow us to obtain short proof another strong convergence theorem problem. also apply our main result fixed point nonexpansive inequality problem...

Variational inequalities are being used as a mathematical programming tool in modeling a wide class of problems arising in different branches of pure and applied sciences, see [1–26]. Variational inequalities have been extended and generalized in various directions using novel and innovative techniques. A useful and important generalization is called the general variational inclusion involving ...

In this paper we study a non-homogeneous elliptic Kirchhoff equation with nonlinear reaction term. We analyze the existence and uniqueness of positive solution. The main novelty is the inclusion of non-homogeneous term making the problem without a variational structure. We use mainly bifurcation arguments to get the results.