SEMI-STABLE AND EXTREMAL SOLUTIONS OF REACTION EQUATIONS INVOLVING THE p-LAPLACIAN

@inproceedings{Sanchn2006SEMISTABLEAE,
title={SEMI-STABLE AND EXTREMAL SOLUTIONS OF REACTION EQUATIONS INVOLVING THE p-LAPLACIAN},
author={Manel Sanch{\'o}n},
year={2006}
}

Manel Sanchón

Published 2006

We consider nonnegative solutions of −∆pu = f(x, u), where p > 1 and ∆p is the p-Laplace operator, in a smooth bounded domain of RN with zero Dirichlet boundary conditions. We introduce the notion of semistability for a solution (perhaps unbounded). We prove that certain minimizers, or one-sided minimizers, of the energy are semi-stable, and study the properties of this class of solutions. Under some assumptions on f that make its growth comparable to um, we prove that every semi-stable… CONTINUE READING