布雷齐斯-尼伦堡问题解的存在性

IF 0.7 4区数学 Q2 MATHEMATICS

Topological Methods in Nonlinear Analysis Pub Date : 2023-01-25 DOI:10.12775/tmna.2022.029

Francisco Odair de Paiva, O. Miyagaki, Adilson E. Presoto

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引用次数: 0

摘要

我们关注的是一个半线性椭圆问题$$\bbegin｛cases｝-\Delta u=\lambda解的存在性_{k}u+在有界域$\Omega\subet\mathbb｛R｝^｛4｝$中，u^3&&\text｛in｝\Omega，\\u=0&&\text{on｝\partial\Omega、\end｛cases｝$$%。这里$\lambda_k$是$H_0^1（\Omega）$中$-\Delta$的特征值。我们证明了这个问题有一个非平凡的解决方案。

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Existence of solutions for the Brezis-Nirenberg problem

We are concerned with of existence of solutions to the semilinear elliptic problem $$ \begin{cases} - \Delta u=\lambda_{k}u+u^3 &\text{in } \Omega, \\ u= 0 &\text{on }\partial \Omega, \end{cases} $$% in a bounded domain $\Omega \subset \mathbb{R}^{4}$. Here $\lambda_k$ is an eigenvalue of the $-\Delta$ in $H_0^1(\Omega)$. We prove that this problem has a nontrivial solution.

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来源期刊

Topological Methods in Nonlinear Analysis 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.