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Journal of Convex Analysis 10 (2003), No. 1, 185--198
Copyright Heldermann Verlag 2003
An Existence Theorem for the Neumann Problem Involving the p-Laplacian
Giovanni Anello
Dept. of Mathematics, University of Messina, 98166 Sant'Agata-Messina, Italy,
anello@dipmat.unime.it
Giuseppe Cordaro
Dept. of Mathematics, University of Messina, 98166 Sant'Agata-Messina, Italy,
cordaro@dipmat.unime.it
We deal with the existence of weak solutions for a Neumann problem
involving the p-Laplacian with asymmetric nonlinearity. We show that
our result gives new conditions on the right hand side which assure the
existence and localization of at least one weak solution. In particular,
we make a comparison with a result obtained in a recent paper by S.
Villegas where he studies the same problem using a different approach.
Keywords: Variational principle, critical point, weak solution, Neumann problem,
p-Laplacian.
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