Electronic Journal of Differential Equations,
Conference 08 (2002), pp. 23-34

Title: Necessary conditions of existence for an elliptic equation with
  source term and measure data involving  $p$-Laplacian

Authors: Marie-Francoise Bidaut-Veron (CNRS UMR, Tours, France)

Abstract: 
We study the  nonnegative solutions to  equation
  $$
   -\Delta_{p}u=u^{q}+\lambda\nu,
  $$
  in a bounded domain $\Omega$ of $\mathbb{R}^{N}$, where $1<p<N$,
  $q>p-1$, $\nu$ is a nonnegative Radon measure on $\Omega$,
  and $\lambda>0$ is a parameter.
  We give necessary conditions on $\nu$ for existence, with
  $\lambda$ small enough, in terms of capacity. We also give a priori
  estimates of the solutions.

Published October 21, 2002.
Math Subject Classifications: 35J70, 35B45, 35D05.
Key Words: Degenerate quasilinear equations; measure data;
capacities; a priori estimates.