Nodal Solutions for Neumann Problems with a Nonhomogeneous Differential Operator

Abstract

We consider a nonlinear elliptic Neumann problem driven by a nonhomogeneous differential operator, which is strictly monotone and incorporates as special cases the p-Laplacian, the (p,q)-differential operator and the generalized p-mean curvature differential operator. Using variational methods coupled with suitable truncation and comparison techniques and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, one positive, the second negative and the third nodal. Also we show that the problem has extremal nontrivial constant sign solutions.