Infinitely many solutions for semilinear Schrödinger equations with sign-changing potential and nonlinearity

In this paper, we study the existence of infinitely many nontrivial solutions for a class of semilinear Schrödinger equations {−△u+V(x)u=f(x,u),x∈RN,u∈H1(RN), where the potential VV is allowed to be sign-changing, and the primitive of the nonlinearity ff is of super-quadratic growth near infinity in uu and is also allowed to be sign-changing. Our super-quadratic growth conditions weaken the Ambrosetti–Rabinowitz type condition.