Ground state solutions of non-linear singular Schrödinger equations with lack of compactness

Abstract

We study a class of time-independent non-linear Schrödinger-type equations on the whole space with a repulsive singular potential in the divergence operator and we establish the existence of non-trivial standing wave solutions for this problem in an appropriate weighted Sobolev space. Such equations have been derived as models of several physical phenomena. Our proofs rely essentially on critical point theory tools combined with the Caffarelli-Kohn-Nirenberg inequality. Copyright © 2003 John Wiley & Sons, Ltd.