6533b7dcfe1ef96bd12719c7
RESEARCH PRODUCT
Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems
Papageorgiou N. S.Vetro C.Vetro F.subject
Settore MAT/05 - Analisi MatematicaNonlinear maximum principleStrong comparisonNodal solutionNonlinear nonhomogeneous differential operatorBifurcation-type theoremCritical groupNonlinear regularity theorydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-01-01 |