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

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