
Journal of Convex Analysis 10 (2003), No. 1, 185198 Copyright Heldermann Verlag 2003 An Existence Theorem for the Neumann Problem Involving the pLaplacian Giovanni Anello Dept. of Mathematics, University of Messina, 98166 Sant'AgataMessina, Italy, anello@dipmat.unime.it Giuseppe Cordaro Dept. of Mathematics, University of Messina, 98166 Sant'AgataMessina, Italy, cordaro@dipmat.unime.it We deal with the existence of weak solutions for a Neumann problem involving the pLaplacian 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, pLaplacian. FullTextpdf (371 K) 