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

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI:10.1515/anona-2021-0221

Gui-Dong Li, Yong-Yong Li, Chunlei Tang

引用次数: 2

Abstract

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.

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Schrödinger方程的无穷多径向和非径向变号解

本文研究了一类Schrödinger方程，它可以表示为-Δu+V（x）u=f（u）， x∈ℝN.-\Δu+V（x）u=f（u），\；\；\；x\在｛\rm｛\mathbb R｝｝^N｝中。如果外电势V是径向的和矫顽的，则我们给出了非线性项f∈C上的局部Ambrosetti-Rabinowitz超线性条件(ℝ, ℝ) 这保证了问题不仅有无限多个径向变符号的解，而且有无限多的非径向变符号解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.