环空超临界Brezis-Nirenberg问题径向正解的唯一性和多重性

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-07-17 DOI:10.1016/j.jde.2025.113621

Naoki Shioji , Satoshi Tanaka , Kohtaro Watanabe

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引用次数: 0

摘要

研究环空中的超临界Brezis-Nirenberg问题。建立了三维情况下径向正解的唯一性结果。并证明了当环空内半径足够小，环空外半径在一定范围内时，问题至少有三个正向径向解。此外，对于每一个正整数k，当方程的指数大于临界Sobolev指数且小于Joseph-Lundgren指数时，问题至少有k个正径向解。

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Uniqueness and multiplicity of positive radial solutions to the super-critical Brezis-Nirenberg problem in an annulus

The super-critical Brezis-Nirenberg problem in an annulus is considered. The new uniqueness result of positive radial solutions is established for the three-dimensional case. It is also proved that the problem has at least three positive radial solutions when the inner radius of the annulus is sufficiently small and the outer radius of the annulus is in a certain range. Moreover, for each positive integer k, the problem has at least k positive radial solutions when the exponent of the equation is greater than the critical Sobolev exponent and is less than the Joseph-Lundgren exponent.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics