On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity
Tom 94 / 2002
Colloquium Mathematicum 94 (2002), 141-150
MSC: 35B33, 35J65, 35J20.
DOI: 10.4064/cm94-1-10
Streszczenie
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.
