Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 26, pp. 1-14.

Title: Existence of solutions to nonlocal elliptic equations 
       with discontinuous terms

Authors: Francisco Julio S. A. Correa (Univ. Federal de Campina Grande, Brazil)
         Rubia G. Nascimento (Univ. Federal do Para, Brazil)

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 07, 2012.
Math Subject Classifications: 35A15, 35J40, 34A36.
Key Words: Variational methods; elliptic problem; 
           discontinuous nonlinearity.