AbstractIn this paper, we study the existence of infinitely many nontrivial solutions for the following semilinear Schrödinger equation: $$ \textstyle\begin{cases} -\Delta u+V(x)u=f(x,u), \quad x\in\mathbb{R}^{N},\\ u\in H^{1}(\mathbb{R}^{N}), \end{cases} $${−Δu+V(x)u=f(x,u),x∈RN,u∈H1(RN), where the potential V is continuous and is allowed to be sign-changing. By using a variant fountain theorem, we obtain the existence of infinitely many high energy solutions under the condition that the nonlinearity $f(x,u)$f(x,u) is of super-linear growth at infinity. The super-quadratic growth condition imposed on $F(x,u)=\int _{0}^{u}f(x,t)\,dt$F(x,u)=∫0uf(x,t)dt is weaker than the Ambrosetti–Rabinowitz type condition and the similar conditions employed in the references.