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.