Abstract

This paper is concerned with the multiplicity of nontrivial solutions in an Orlicz-Sobolev space for a nonlocal problem involving N-functions and theory of locally Lispchitz continuous functionals. More precisely, in this paper, we study a result of multiplicity to the following multivalued elliptic problem: {−M(∫ΩΦ(∣∇u∣)dx)div(ϕ(∣∇u∣)∇u)−ϕ(∣u∣)u∈∂F(u) in Ω,u∈W01LΦ(Ω),\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) \ \text{in}\ \Omega,\\[6mm] u\in W_0^1L_\Phi(\Omega), \end{array} \right. where Ω⊂RN\Omega\subset\mathbb{R}^{N} is a bounded smooth domain, N≥2N\geq 2, MM is continuous function, Φ\Phi is an N-function with Φ(t)=∫0∣t∣ϕ(s)s ds\Phi(t)=\displaystyle\int^{|t|}_{0}\phi(s)s \ ds and ∂F(t)\partial F(t) is a generalized gradient of F(t)F(t). We use genus theory to obtain the main result

Author information

Contact details are reproduced from the original publication and may be historical.

Giovany M. Figueiredo

Universidade Federal do Pará, Faculdade de Matemática, 66075-110 Belém - Pa, Brazil

giovany@ufpa.br

Jefferson A. Santos

Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática e Estatística, 58109-970 Campina Grande - PB, Brazil

jefferson@dme.ufcg.edu.br

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Suggested citation

G. M. Figueiredo, J. A. Santos. “On a Nonlocal Multivalued Problem in an Orlicz-Sobolev Space via Krasnoselskii's Genus.” Journal of Convex Analysis 22 (2015), No. 2, 447–464. https://doi.org/10.68381/jca22020

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