Existence and multiplicity of nontrivial solutions for a class of semilinear fractional Schrödinger equations (Q1674071)

Summary: This paper is concerned with the existence of solutions to the following fractional Schrödinger type equations: \((-\Delta)^su+V(x)u=f(x,u)\), \(x\in R^N\), where the primitive of the nonlinearity \(f\) is of superquadratic growth near infinity in \(u\) and the potential \(V\) is allowed to be sign-changing. By using variant Fountain theorems, a sufficient condition is obtained for the existence of infinitely many nontrivial high energy solutions.