具有临界增长的薛定谔方程的新型解决方案

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-08-21 DOI:10.1063/5.0206967

Yuan Gao, Yuxia Guo

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引用次数: 0

摘要

我们考虑以下具有临界增长的非线性薛定谔方程：-Δu+V(|y|)u=uN+2N-2,u>0inRN，其中 V(|y|) 是 C1 中的有界正径向函数，N ≥ 5。通过有限还原论证，我们证明如果 r2V(r) 在 r0 > 0 处有孤立局部最大值或孤立局部最小值，且 V(r0) > 0，则存在无限多的非径向大能量解，这些解在 O(3) 的一些子群下是不变的。

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New type of solutions for Schrödinger equations with critical growth

We consider the following nonlinear Schrödinger equations with critical growth: −Δu+V(|y|)u=uN+2N−2,u>0inRN, where V(|y|) is a bounded positive radial function in C1, N ≥ 5. By using a finite reduction argument, we show that if r2V(r) has either an isolated local maximum or an isolated local minimum at r0 > 0 with V(r0) > 0, there exists infinitely many non-radial large energy solutions which are invariant under some sub-groups of O(3).

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

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