Electron. J. Diff. Equ., Vol. 2012 (2012), No. 26, pp. 1-14.

Existence of solutions to nonlocal elliptic equations with discontinuous terms

Francisco Julio S. A. Correa, Rubia G. Nascimento

Abstract:
In this article, we study the existence of nonnegative solutions for the elliptic partial differential equation
$$\displaylines{ -[M(\|u\|^{p}_{1,p})]^{1,p}\Delta_{p}u = f(x,u) \quad\hbox{in } \Omega , \cr u = 0 \quad\hbox{on } \partial\Omega , }$$
where $\Omega \subset \mathbb{R}^N$ is a bounded smooth domain, $f:\overline{\Omega}\times \mathbb{R}^+\to \mathbb{R}$ is a discontinuous nonlinear function.

Submitted October 12, 2011. Published February 7, 2012.
Math Subject Classifications: 35A15, 35J40, 34A36.
Key Words: Variational methods; elliptic problem; discontinuous nonlinearity.

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Francisco Julio S. A. Corrêa
Universidade Federal de Campina Grande
Unidade Acadêmica de Matemática e Estatística
CEP:58109-970, Campina Grande-PB, Brazil
email: fjsacorrea@gmail.com
Rubia G. Nascimento
Faculdade de Matemática
Universidade Federal do Pará
CEP:66075-110, Belém -PA, Brazil
email: rubia@ufpa.br

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