Strongly nonlinear multivalued elliptic equations on a bounded domain

Claudianor Alves (), José Gonçalves () and Jefferson Santos ()

Journal of Global Optimization, 2014, vol. 58, issue 3, 565-593

Abstract: In this work we study the existence of nontrivial solution for the following class of multivalued quasilinear problems $$\begin{aligned} \displaystyle -\text{ div } ( \phi (|\nabla u|) \nabla u) - b(u)u \in \lambda \partial F(x,u)\;\text{ in }\;\Omega , \quad u=0\; \text{ on }\;\partial \Omega \end{aligned}$$ where $$\Omega \subset \mathbb{R }^N$$ is a bounded domain, $$N\ge 2$$ and $$\partial F(x,u)$$ is a generalized gradient of $$F(x,t)$$ with respect to $$t$$ . The main tools utilized are Variational Methods for Locally Lipschitz Functional and a Concentration Compactness Theorem for Orlicz space. Copyright Springer Science+Business Media New York 2014

Keywords: Quasilinear equations; Critical exponents; Non-smooth functionals; Orlicz-Sobolev; 35A15; 35J25; 34A36 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10898-013-0052-3

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