We study the spectrum of the Poincaré variational problem for two close to touching inclusions in IR. We derive the asymptotics of its eigenvalues as the distance between the inclusions tends to zero.

In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.

‎This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...

In this article, we introduce a new general iterative method for finding a common element of the set of solutions generalized for mixed equilibrium problems, the set of solution for fixed point for nonexpansive mappings and the set of solutions for the variational inclusions for b1, b2-inverse-strongly monotone mappings in a real Hilbert space. We prove that the sequence converges strongly to a...

In this paper, we find a class of special inclusions that have the same property with respect to second order linear partial differential equations as holds for ellipsoids. That is, in the simplest case and in physical terms, constant magnetization of the inclusion implies constant magnetic field on the inclusion. The special inclusions are found as solutions of a simple variational inequality....

Variational inequality methods whether based on numerous available new algorithms or otherwise have been applied vigorously, especially to model equilibria problems in economics, optimization and control theory, operations research, transportation network modeling, and mathematical programming, while a considerable progress to developing general methods for the sensitivity analysis for variatio...

For a general category of variational inclusions in finite dimensions, a class of parameterizations, called " ample " parameterizations, is identified that is rich enough to provide a full theory of Lipschitz-type properties of solution mappings without the need for resorting to the auxiliary introduction of canonical parameters. Ample parameterizations also support a detailed description of th...

The paper is devoted to optimization problems of the Bolza and Mayer types for evolution systems governed by nonconvex Lipschitzian differential inclusions in Banach spaces under endpoint constraints described by finitely many equalities and inequalities. with generally nonsmooth functions. We develop a variational analysis of such problems mainly based on their discrete approximations and the ...