On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity

Volume 94 / 2002

J. Chabrowski, Shusen Yan Colloquium Mathematicum 94 (2002), 141-150 MSC: 35B33, 35J65, 35J20. DOI: 10.4064/cm94-1-10


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.


  • J. ChabrowskiDepartment of Mathematics
    University of Queensland
    St. Lucia, Qld 4072, Australia
  • Shusen YanSchool of Mathematics and Statistics
    University of Sydney
    Sydney, NSW 2006, Australia

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