
Journal of Convex Analysis 22 (2015), No. 2, 447464 Copyright Heldermann Verlag 2015 On a Nonlocal Multivalued Problem in an OrliczSobolev Space via Krasnoselskii's Genus Giovany M. Figueiredo Universidade Federal do Pará, Faculdade de Matemática, 66075110 Belém  Pa, Brazil giovany@ufpa.br Jefferson A. Santos Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática e Estatística, 58109970 Campina Grande  PB, Brazil jefferson@dme.ufcg.edu.br [Abstractpdf] This paper is concerned with the multiplicity of nontrivial solutions in an OrliczSobolev space for a nonlocal problem involving Nfunctions and theory of locally Lispchitz continuous functionals. More precisely, in this paper, we study a result of multiplicity to the following multivalued elliptic problem: $$ \left \{ \begin{array}{l} M\left(\displaystyle\int_\Omega \Phi(\mid\nabla u\mid)dx\right) div\big(\phi(\mid\nabla u\mid)\nabla u\big) \phi(u)u\in \partial F(u) \ \mbox{in}\ \Omega,\\[6mm] u\in W_0^1L_\Phi(\Omega), \end{array} \right. $$ where $\Omega\subset\mathbb{R}^{N}$ is a bounded smooth domain, $N\geq 2$, $M$ is continuous function, $\Phi$ is an Nfunction with $\Phi(t)=\displaystyle\int^{t}_{0}\phi(s)s \ ds$ and $\partial F(t)$ is a generalized gradient of $F(t)$. We use genus theory to obtain the main result. [ Fulltextpdf (180 KB)] for subscribers only. 