Remarks on infinitely many solutions for a class of Schrödinger equations with sublinear nonlinearity

Abstract

In this paper, we study the existence of multiple nontrivial solutions for the following semilinear Schrödinger equation: {array−Δu+V(x)u=f(x,u),x∈ℝN,arrayu∈H1(ℝN), where the potential V is continuous and allowed to be sign‐changing and f(x,u) satisfies more general sublinear growth conditions than those in previous studies. The first result of this paper obtains the existence of a nontrivial solution of (). The second establishes an existent result on infinitely many nontrivial solutions of () by using a variant fountain theorems.