Multiple positive standing wave solutions for schrödinger equations with oscillating state-dependent potentials

Abstract

Motivated by relevant physical applications, we study Schrodinger equations with state-dependent potentials. Existence, localization and multiplicity results are established for positive standing wave solutions in the case of oscillating potentials. To this aim, a localized Pucci-Serrin type critical point theorem is first obtained. Two examples are then given to illustrate the new theory.