An Existence Theorem for the Neumann Problem Involving the p-Laplacian

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.