Infinitely many radial and non-radial sign-changing solutions for Schrödinger equations

Abstract

Abstract In the present paper, a class of Schrödinger equations is investigated, which can be stated as − Δ u + V ( x ) u = f ( u ) ,         x ∈ ℝ N . - \Delta u + V(x)u = f(u),\;\;\;\;x \in {{\rm{\mathbb R}}^N}. If the external potential V is radial and coercive, then we give the local Ambrosetti-Rabinowitz super-linear condition on the nonlinearity term f ∈ C(ℝ, ℝ) which assures the problem has not only infinitely many radial sign-changing solutions, but also infinitely many non-radial sign-changing solutions.