Multiplicity and symmetry breaking for supercritical elliptic problems in exterior domains

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-09-09 DOI:10.1088/1361-6544/ad74d0

Alberto Boscaggin, Francesca Colasuonno, Benedetta Noris, Tobias Weth

引用次数: 0

Abstract

We deal with the following semilinear equation in exterior domains

−Δu+u=a(x)|u|p−2u,u∈H01(AR),

where

AR:={x∈RN:|x|>R}

N⩾3

, R > 0. Assuming that the weight a is positive and satisfies some symmetry and monotonicity properties, we exhibit a positive solution having the same features as a, for values of p > 2 in a suitable range that includes exponents greater than the standard Sobolev critical one. In the special case of radial weight a, our existence result ensures multiplicity of nonradial solutions. We also provide an existence result for supercritical p in nonradial exterior domains.

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外域超临界椭圆问题的多重性和对称性突破

我们处理的是外部域中的半线性方程 -Δu+u=a(x)|u|p-2u,u∈H01(AR)，其中 AR:={x∈RN:|x|>R}, N⩾3, R > 0。假定权重 a 为正值，并满足一些对称性和单调性特性，对于 p > 2 的取值范围（包括大于标准索波列夫临界值的指数），我们展示了与 a 具有相同特征的正解。在径向权 a 的特殊情况下，我们的存在性结果确保了非径向解的多重性。我们还提供了非径向外部域中超临界 p 的存在性结果。

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

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.