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

Abstract

In the present paper, a class of Schrödinger equations is investigated, which can be stated as −Δu+V(x)u=f(u), x∈ℝN.- \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.

Keywords

• schrödinger equation
• radial sign-changing solutions
• non-radial sign-changing solutions
• variational methods
• principle of symmetric criticality
• invariant sets of descending flow
• 35a15
• 35d30
• 35j10
• 35j20