1Department of Mathematics University of Queensland St. Lucia, Qld 4072, Australia 2School of Mathematics and Statistics University of Sydney Sydney, NSW 2006, Australia
Colloquium Mathematicum, Tome 94 (2002) no. 1, pp. 141-150
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.
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
Affiliations des auteurs :
J. Chabrowski
1
;
Shusen Yan
2
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
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J. Chabrowski; Shusen Yan. On the nonlinear Neumann problem at resonance
with critical Sobolev nonlinearity. Colloquium Mathematicum, Tome 94 (2002) no. 1, pp. 141-150. doi: 10.4064/cm94-1-10
