Existence of solutions for some nonlinear elliptic equations

Abstract

In this paper, we study the existence of solutions to the following nonlinear elliptic problem in a bounded subset $Omega$ of $mathbb{R}^{N}$: $$displaylines{ -Delta _{p}u = f(x,u, abla u)+mu quad hbox{in } Omega ,cr u = 0 quad hbox{on }partial Omega , }$$ where $mu $ is a Radon measure on $Omega $ which is zero on sets of $p$-capacity zero, $f:Omega imes mathbb{R}imes mathbb{R} ^{N}o mathbb{R}$ is a Caratheodory function that satisfies certain conditions with respect to the one dimensional spectrum.

Keywords

• Boundary value problem
• truncation
• p-Laplacian
• spectrum.