Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 63, pp. 1-13.
Title: Existence of solutions for some nonlinear elliptic equations
Authors: Aomar Anane (Univ. Mohammed 1er, Oujda, Maroc)
Omar Chakrone (Univ. Mohammed 1er, Oujda, Maroc)
Mohammed Chehabi (Univ. Mohammed 1er, Oujda, Maroc)
Abstract:
In this paper, we study the existence of solutions to the following
nonlinear elliptic problem in a bounded subset $\Omega$ of
$\mathbb{R}^{N}$:
$$\displaylines{
-\Delta _{p}u = f(x,u,\nabla u)+\mu \quad \hbox{in } \Omega ,\cr
u = 0 \quad \hbox{on }\partial \Omega ,
}$$
where $\mu $ is a Radon measure on $\Omega $ which is zero on
sets of $p$-capacity zero,
$f:\Omega \times \mathbb{R}\times \mathbb{R} ^{N}\to \mathbb{R}$
is a Caratheodory function that satisfies certain
conditions with respect to the one dimensional spectrum.
Submitted January 23, 2006. Published May 19,2006.
Math Subject Classifications: 35J15, 35J70, 35J85.
Key Words: Boundary value problem; truncation; p-Laplacian; spectrum.