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.

中文翻译：

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薛定谔方程的无限多个径向和非径向符号变化解

本文研究了一类薛定谔方程，可表示为-Δu+V(x)u=f(u)，x∈ℝN。- \Delta u + V(x)u = f(u),\;\;\;\;x \in {{\rm{\mathbb R}}^N}。如果外部势 V 是径向和矫顽的，那么我们在非线性项 f ∈ C (ℝ, ℝ) 上给出局部 Ambrosetti-Rabinowitz 超线性条件，这确保问题不仅具有无限多个径向符号变化解，而且也有无穷多个非径向符号改变解。