Work

Multiple solutions for the Brezis-Nirenberg problem

Year: 2005

Type: article

Abstract: We establish the existence of multiple solutions to the Dirichlet problem for the equation \[ -\Delta u=\lambda u+|u|^{\frac{4}{N-2}}u \] on a bounded domain $\Omega$ of $\mathbb{R}^{N},$ $N\geq4.$ We show that, if $\lambda>0$ is not a Dirichlet eigenvalue of $-\Delta$ on $\Omega,$ this problem has at least $\frac{N+1}{2}$ pairs of nontrivial solutions. If $\lambda$ is an eigenvalue of multiplicity $m$ then it has at least $\frac{N+1-m}{2}$ pairs of nontrivial solutions.

Source: Advances in Differential Equations

DOI: 10.57262/ade/1355867873

Authors: Mónica Clapp, Tobias Weth

Institutions: Justus-Liebig-Universität Gießen, Universidad Nacional Autónoma de México

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Deutsche Forschungsgemeinschaft

Award: G6085131044