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.