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Existence, Stability and Oscillation Properties of Slow-Decay Positive Solutions of Supercritical Elliptic Equations with Hardy Potential

Published online by Cambridge University Press:  16 April 2014

Vitaly Moroz
Affiliation:
Department of Mathematics, Swansea University, Singleton Park, Swansea SA2 8PP, UK, ([email protected])
Jean van Schaftingen
Affiliation:
Institut de Recherche en Mathématique et Physique (IRMP), Université catholique de Louvain, Chemin du Cyclotron 2 bte L7.01.01, 1348 Louvain-la-Neuve, Belgium, ([email protected])

Abstract

We prove the existence of a family of slow-decay positive solutions of a supercritical elliptic equation with Hardy potential

and study the stability and oscillation properties of these solutions. We also show that if the equation on ℝN has a stable slow-decay positive solution, then for any smooth compact K ⊂ ℝN a family of the exterior Dirichlet problems in ℝN \ K admits a continuum of stable slow-decay infinite-energy solutions.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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