an:01968257
Zbl 1091.35026
Anello, Giovanni; Cordaro, Guiseppe
An existence theorem for the Neumann problem involving the \(p\)-Laplacian
EN
J. Convex Anal. 10, No. 1, 185-198 (2003).
00092748
2003
j
35J60 35D05 35J25
Variational principle; critical point; weak solution; Neumann problem; \(p\)-Laplacian.
Summary: 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 \textit{S. Villegas} [J. Differ. Equations 145, No. 1, 145--155 (1998; Zbl 0910.34035)] where he studies the same problem using a different approach.
Zbl 0910.34035