Nodal solutions for nonlinear nonhomogeneous Neumann equations

Abstract

We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator with a Caratheodory reaction which is $(p-1)$-sublinear near $\pm\infty$. Using variational tools we show that the problem has at least three nontrivial smooth solutions (one positive, one negative and a third nodal). Our formulation unifies problems driven by the $p$-Laplacian, the $(p,q) $ Laplacian and the $p$-generalized mean curvature operator.