On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity

J. Chabrowski¹ ; Shusen Yan²

¹ Department of Mathematics University of Queensland St. Lucia, Qld 4072, Australia
² School of Mathematics and Statistics University of Sydney Sydney, NSW 2006, Australia

Colloquium Mathematicum, Tome 94 (2002) no. 1, pp. 141-150.

Résumé

We consider the Neumann problem for the equation $-{\mit \Delta } u-\lambda u = Q(x)|u|^{2^{*}-2}u$, $u\in H^1({\mit \Omega })$, where $Q$ is a positive and continuous coefficient on $\hskip 1.8pt\overline {\hskip -1.8pt{\mit \Omega }\hskip -.2pt}\hskip .2pt$ and $\lambda $ is a parameter between two consecutive eigenvalues $\lambda _{k-1}$ and $\lambda _k$. Applying a min-max principle based on topological linking we prove the existence of a solution.

Détail

DOI : 10.4064/cm94-1-10

Keywords: consider neumann problem equation mit delta u lambda * mit omega where positive continuous coefficient hskip overline hskip mit omega hskip hskip lambda parameter between consecutive eigenvalues lambda k lambda applying min max principle based topological linking prove existence solution