Electron. J. Diff. Equ., Vol. 2012 (2012), No. 35, pp. 1-18.

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

Nedra Belhaj Rhouma, Wahid Sayeb

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.

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Nedra Belhaj Rhouma
Departement de Mathématiques, Facultédes sciences de Tunis
Université Tunis El Manar
Campus Universitaire 2092, Tunis, Tunisia
email: nedra.belhajrhouma@fst.rnu.tn
Wahid Sayeb
Departement de Mathématiques, Facultédes sciences de Tunis
Université Tunis El Manar
Campus Universitaire 2092, Tunis, Tunisia
email: wahid.sayeb@yahoo.fr

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