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.