Positive solutions of a Neumann problem with competing critical nonlinearities

Jan Chabrowski, Stathis Filippas, Achilles Tertikas

DOI: http://dx.doi.org/10.12775/TMNA.2006.017

Abstract


We present existence results for a Neumann problem involving
critical Sobolev nonlinearities both on the right hand side of
the equation and at the boundary condition. Positive
solutions are obtained through constrained minimization on the
Nehari manifold. Our approach is based on the concentration
compactness principle of P. L. Lions and M. Struwe.

Keywords


Neumann problem; Sobolev critical exponents; constrained minimization; concentration phenomena; Nehari manifold; least energy solutions

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