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.

Papageorgiou N.S., Vetro C., Vetro F. (2020). Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 1-20.

Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems

Vetro C.;
2020-01-01

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.
Settore MAT/05 - Analisi Matematica
https://ejde.math.txstate.edu/Volumes/2020/12/papageorgiou.pdf
Papageorgiou N.S., Vetro C., Vetro F. (2020). Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 1-20.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/401402
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