Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems
- Autori: Papageorgiou N.S.; Vetro C.; Vetro F.
- Anno di pubblicazione: 2020
- Tipologia: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/401402
Abstract
We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter λ > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution.