Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems

We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is ( p - 1 ) -superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation...

Full description

Saved in:
Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2020, Vol.114 (1)
Main Authors: Papageorgiou, Nikolaos S., Vetro, Calogero, Vetro, Francesca
Format: Article
Language:English
Subjects:
Applications of Mathematics
Bifurcations
Differential equations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Original Paper
Parameters
Theoretical
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is ( p - 1 ) -superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter λ > 0 varies. Also we prove the existence of a minimal positive solution u λ ∗ and determine the monotonicity and continuity properties of the map λ → u λ ∗ .
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-019-00779-1