Energy solutions and concentration problem of fractional Schrödinger equation

Abstract

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.

Keywords

• Fractional Schrödinger equations
• Steep potential well
• Sublinear perturbation
• Infinitely many high or small energy solutions
• Concentration of solutions