Infinitely many solutions for semilinear Schrِdinger 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 ∈ R N , u ∈ H 1 ( R N ) , where the potential V is allowed to be sign-changing, and the primitive of the nonlinearity f is of super-quadratic growth near infinity in u and is also allowed to be sign-changing. Our super-quadratic growth conditions weaken the Ambrosetti–Rabinowitz type condition.