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

In this article, we study the existence of nonnegative solutions for the elliptic partial differential equation
 -[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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