Single‐peak solutions for a subcritical Schrödinger equation with non‐power nonlinearity

Abstract

This paper deals with the following slightly subcritical Schrödinger equation: where is a nonnegative smooth function, , , , . Most of the previous works for the Schrödinger equations were mainly investigated for power‐type nonlinearity. In this paper, we will study the case when the nonlinearity is a non‐power nonlinearity. We show that, for ε small enough, there exists a family of single‐peak solutions concentrating at the positive stable critical point of the potential .