Necessary conditions of existence for an elliptic equation with source term and measure data involving p-Laplacian
Marie‐Françoise Bidaut‐Véron · DOAJ (DOAJ: Directory of Open Access Journals) · 2002
We study the nonnegative solutions to equation $$ -Delta_{p}u=u^{q}+lambdau, $$ in a bounded domain $Omega$ of $mathbb{R}^{N}$, where $1 p-1$, $u$ is a nonnegative Radon measure on $Omega$, and $lambda>0$ is a parameter. We give necessary conditions on $u$ for existence, with $lambda$ small enough, in terms of capacity. We also give a priori estimates of the solutions.