Positive and nodal solutions for nonlinear nonhomogeneous parametric Neumann problems
Date
2020-01-24
Authors
Papageorgiou, Nikolaos S.
Vetro, Catogero
Vetro, Francesca
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Nonlinear nonhomogeneous differential operator, Nonlinear Regularity Theory, Nonlinear maximum principle, Strong comparison, Bifurcation-type theorem, Nodal solution, Critical group
Citation
Papageorgiou, 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.
Rights
Attribution 4.0 International