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$% J. Chabrowski, On the nonlinear Neumann problem involving the critical Sobolev exponent and Hardy potential, Rev. Mat. Complut. 17 (2004), 195–227.%$

On the Nonlinear Neumann Problem Involving the Critical Sobolev Exponent and Hardy Potential

Jan CHABROWSKI
Department of Mathematics,
University of Queensland
St. Lucia 4072, Qld — Australia
jhc@maths.uq.edu.au

Received: September 9, 2003
Accepted: October 30, 2003
ABSTRACT

In this paper we investigate the solvability of some Neumann problems involving the critical Sobolev and Hardy exponents. It is assumed that the coefficient Q is a positive and smooth function on _O_, m and c are real parameters. We examine the common effect of the mean curvature of the boundary @_O_, the shape of the graph of the coefficient Q and the singular Hardy potential on the existence and the nonexistence of solutions of these problems.

Key words: Neumann problem, critical Sobolev exponent, singular Hardy potential, least energy solutions, topological linking.
2000 Mathematics Subject Classification: 35B33, 35J20, 35J65.