# A multiplicity result for an elliptic anisotropic differential inclusion involving variable exponents

 Title A multiplicity result for an elliptic anisotropic differential inclusion involving variable exponents Publication Type Journal Article Authors Costea, Nicusor, and Gheorghe Morosanu Journal title Set-Valued and Variational Analysis Year 2013 Pages 311-322 Volume 21 Abstract In this paper we are concerned with the study of a class of quasilinear elliptic diff erential inclusions involving the anisotropic $\overrightarrow{p}(\cdot)$-Laplace operator, on a bounded open subset of $IR^n$ which has a smooth boundary. The abstract framework required to study this kind of di erential inclusions lies at the interface of three important branches in analysis: nonsmooth analysis, the variable exponent Lebesgue-Sobolev spaces theory and the anisotropic Sobolev spaces theory. Using the concept of nonsmooth critical point we are able to prove that our problem admits at least two non-trivial weak solutions. ISSN 1877-0533 Language English Publisher link http://mathematics.ceu.hu/sites/default/files/field_attachment/page/node-19269/costea-morosanu-preprint-version.pdf
Unit:
Department of Mathematics and its Applications