具有收缩吸引力区域的半线性椭圆方程的正极限和节点极限剖面

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-10-22 DOI:10.1016/j.na.2024.113680

Mónica Clapp , Víctor Hernández-Santamaría , Alberto Saldaña

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引用次数: 0

摘要

我们研究了在任意形状的收缩自聚焦核心存在的情况下，薛定谔方程正解和节点解的存在与集中。通过适当的重定标，这种集中会产生一个极限轮廓，该轮廓可以求解一个非自主椭圆半线性方程，其非线性符号会发生急剧变化。我们描述了（径向或叶状施瓦茨）对称性以及最小能量正向和节点极限剖面的（多项式）衰减。

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Positive and nodal limiting profiles for a semilinear elliptic equation with a shrinking region of attraction

We study the existence and concentration of positive and nodal solutions to a Schrödinger equation in the presence of a shrinking self-focusing core of arbitrary shape. Via a suitable rescaling, the concentration gives rise to a limiting profile that solves a nonautonomous elliptic semilinear equation with a sharp sign change in the nonlinearity. We characterize the (radial or foliated Schwarz) symmetries and the (polynomial) decay of the least-energy positive and nodal limiting profiles.

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来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.