Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 35, pp. 1-18.

Title: Existence of solutions for the p-Laplacian involving a Radon measure

Authors: Nedra Belhaj Rhouma (Univ. Tunis El Manar, Tunisia)
         Wahid Sayeb (Univ. Tunis El Manar, Tunisia)
	 
Abstract:
 In this article we study the existence of solutions to eigenvalue problem
 $$\displaylines{
 -\hbox{div} (|\nabla u|^{p-2}\nabla u)-\lambda |u|^{p-2}u\mu=f \quad
 \hbox{in }\Omega,\cr
 u=0\quad\hbox{on }\partial\Omega
 }$$
 where $\Omega$ is a bounded domain in $\mathbb{R}^N$ and $\mu$ is a
 nonnegative Radon measure.

Submitted June 11, 2011. Published February 29, 2012.
Math Subject Classifications: 34B15, 34B18, 35A01, 35A02.
Key Words: Dirichlet problem; p-Laplacian; genus function;  eigenfunction;
           nonlinear eigenvalue problem; Palais-Smale condition;
           mountain-pass theorem; critical point.