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引用次数: 0
摘要
本文涉及以下非线性椭圆方程:$$ -\Delta u=Q(|y'|,y'')u^{frac{N+2}{N-2}},\,\,u>0,\,\,\text{in}\,{ \mathbb{R}}^{N},\,\,u\in D^{1,2}({\mathbb{R}}^{N}), $$ 其中$(y'、y'')\in {\mathbb{R}}^{2}\times {\mathbb{R}}^{N-2}$ , $N\geq 5$ , $Q(|y'|,y'')$ 是 $\mathbb{R}^{2}\times {\mathbb{R}}^{N-2}$ 中的有界非负函数。通过使用局部 Pohozaev 特性,我们证明了 (Peng et al. in J. Differ. Equ. 267:2503-2530, 2019) 中构建的正解的非退化结果。
Nondegeneracy of the solutions for elliptic problem with critical exponent
This paper deals with the following nonlinear elliptic equation: $$ -\Delta u=Q(|y'|,y'')u^{\frac{N+2}{N-2}},\,\,u>0,\,\,\text{in}\,{ \mathbb{R}}^{N},\,\,u\in D^{1,2}({\mathbb{R}}^{N}), $$ where $(y',y'')\in {\mathbb{R}}^{2}\times {\mathbb{R}}^{N-2}$ , $N\geq 5$ , $Q(|y'|,y'')$ is a bounded nonnegative function in $\mathbb{R}^{2}\times {\mathbb{R}}^{N-2}$ . By using the local Pohozaev identities we prove a nondegeneracy result for the positive solutions constructed in (Peng et al. in J. Differ. Equ. 267:2503–2530, 2019).
期刊介绍:
The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.