  We consider a nonlinear Neumann problem driven by a $p$-Laplacian-type,
nonhomogeneous elliptic differential operator and a Carath\'eodory reaction
term. In this paper we prove the existence of two extremal constant sign smooth
solutions and a nontrivial nodal smooth solution. In the proof we use
variational methods with truncation techniques, critical point theory and Morse
theory (critical groups).

Analysis of PDEs