Energy solutions and concentration problem of fractional Schrödinger equation

Abstract

In this paper, we consider a fractional Schrödinger equation with steep potential well and sublinear perturbation. By virtue of variational methods, the existence criteria of infinitely many nontrivial high or small energy solutions are established. In addition, the phenomenon of the concentration of solutions is also explored. We also give some examples to demonstrate the main results. MSC: 26A33; 35A15; 35B20

Infinitely many solutions for fractional Schrödinger equation with potential vanishing at infinity

“…[16]) Let X be a Banach space. If the functional I λ (u) satisfies: (B1) For λ ∈[1,2], I λ (u) maps bounded sets into bounded sets uniformly and…”