Existence Results for Nonlocal and Nonsmooth Hemivariational Inequalities
نویسندگان
چکیده
We consider an elliptic hemivariational inequality with nonlocal nonlinearities. Assuming only certain growth conditions on the data, we are able to prove existence results for the problem under consideration. In particular, no continuity assumptions are imposed on the nonlocal term. The proofs rely on a combined use of recent results due to the authors on hemivariational inequalities and operator equations in partially ordered sets.
منابع مشابه
Existence and Uniqueness Results for a Nonstandard Variational-Hemivariational Inequalities with Application
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...
متن کاملHistory-dependent hemivariational inequalities with applications to Contact Mechanics
In this paper we survey some of our recent results on the existence and uniqueness of solutions to nonconvex and nonsmooth problems which arise in Contact Mechanics. The approach is based on operator subdifferential inclusions and hemivariational inequalities, and focuses on three aspects. First, we report on results on the second order history-dependent subdifferential inclusions and hemivaria...
متن کاملSemilinear Hemivariational Inequalities with Strong Resonance at Infinity
A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and extend results in the literature, two results on existence are obtained.
متن کاملModeling, analysis and optimal control of systems described by hemivariational inequalities
In the paper we present a survey on the mathematical modeling of nonconvex and nonsmooth problems arising in the mathematical theory of contact mechanics which is a growing field in engineering and scientific computing. The approach to such problems is based on the notion of hemivariational inequality and our presentation focuses on three aspects. First we present the ideas leading to inequalit...
متن کاملMULTIPLE SOLUTIONS FOR SEMILINEAR HEMIVARIATIONAL INEQUALITIES AT RESONANCE By LESZEK GASI\’{N}SKI AND NIKOLAOS
Abstract. We consider semilinear eigenvalue problems for hemivariational inequalities at resonance. First we consider problems which are at resonance in a higher eigenvalue $\lambda_{k}$ (with $k\geq 1$ ) and prove two multiplicity theorems asserting the existence of at least $k$ pairs of nontrivial solutions. Then we consider problems which are resonant at the first eigenvalue $\lambda_{1}>0$ ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006