Measure data problems for a class of elliptic equations with mixed absorption-reaction

Abstract

We study the existence of nonnegative solutions to the Dirichlet problem $\CL^{_{^M}}_{p,q}u:=-Δu+u^p-M|\nabla u|^q=μ$ in a domain $Ω\subset\BBR^N$ where $\mu$ is a nonnegative Radon measure, when $p>1$, $q>1$ and $M\ge 0$. We also give conditions under which nonnegative solutions of $\CL^{_{^M}}_{p,q}u=0$ in $\Omega \setminus K$ where $K$ is a compact subset of $\Omega$ can be extended as a solution of the same equation in $\Omega$

26 pages