一类奇异椭圆型方程变号解的存在性及非存在性

彭艳芳, 李必文

数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 281-294.

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数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 281-294. DOI: 10.12386/A2014sxxb0028
论文

一类奇异椭圆型方程变号解的存在性及非存在性

    彭艳芳1, 李必文2
作者信息 +

Existence and Nonexistence of Sign-Changing Solutions for a Singular Elliptic Problem

    Yan Fang PENG1, Bi Wen LI2
Author information +
文章历史 +

摘要

考虑了一类与Caffarelli-Kohn-Nirenberg不等式有关的奇异椭圆型方程

利用 Ljusternik-Schnirelaman 理论及一个Pohozaev型恒等式,证明了上述方程变号解的存在性及非存在性.

Abstract

We consider the following singular elliptic equation
,
which involves the Caffarelli-Kohn-Nirenberg inequalities. By virtue of the Ljusternik-Schnirelaman theory and a Pohozaev-type identity, we obtain the existence and nonexistence results of sing-changing solutions for the above problem.

关键词

变号解 / 解的存在性及非存在性 / 奇异性

Key words

sign-changing solution / existence and nonexistence of solutions / singularity

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导出引用
彭艳芳, 李必文. 一类奇异椭圆型方程变号解的存在性及非存在性. 数学学报, 2014, 57(2): 281-294 https://doi.org/10.12386/A2014sxxb0028
Yan Fang PENG, Bi Wen LI. Existence and Nonexistence of Sign-Changing Solutions for a Singular Elliptic Problem. Acta Mathematica Sinica, Chinese Series, 2014, 57(2): 281-294 https://doi.org/10.12386/A2014sxxb0028

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基金

贵州省科学技术基金资助项目(黔科合J字LKS[2013]03号)

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