Existence of solutions for the Brezis-Nirenberg problem
DOI:
https://doi.org/10.12775/TMNA.2022.029Keywords
Critical growth, resonance, low dimensionAbstract
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.References
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Copyright (c) 2023 Francisco Odair de Paiva, Olímpio H. Miyagaki, Adilson E. Presoto
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