Papageorgiou, Nikolaos S.Vetro, CatogeroVetro, Francesca2021-09-212021-09-212020-01-24Papageorgiou, N. S., Vetro, C., & Vetro, F. (2020). Positive and nodal solutions for nonlinear nonhomogeneous parametric Neumann problems. <i>Electronic Journal of Differential Equations, 2020</i>(12), pp. 1-20.1072-6691https://hdl.handle.net/10877/14516We 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.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear nonhomogeneous differential operatorNonlinear Regularity TheoryNonlinear maximum principleStrong comparisonBifurcation-type theoremNodal solutionCritical groupArticle