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

Abstract

In this article we study the existence of solutions to eigenvalue problem $$displaylines{ -hbox{div} (|abla u|^{p-2}abla u)-lambda |u|^{p-2}umu=f quad hbox{in }Omega,cr u=0quadhbox{on }partialOmega }$$ where $Omega$ is a bounded domain in $mathbb{R}^N$ and $mu$ is a nonnegative Radon measure.

Keywords

• Dirichlet problem
• p-Laplacian
• genus function
• eigenfunction
• nonlinear eigenvalue problem
• Palais-Smale condition
• mountain-pass theorem
• critical point