Orbital Stability for the Schrödinger Operator Involving Inverse Square Potential

Abstract

In this paper we prove the existence of orbitally stable standing waves for the critical Schrödinger operator, involving potential of the form ${\left(\frac{N-2}{2}\right)}^2|x{|}^{-2}$. The approach, being purely variational, is based on the precompactness of any minimizing sequence with respect to the associated energy. Moreover, we discuss the case of the presence of a Hardy energy term, in conjunction with the behavior of the standing waves at the singularity.

21 pages