Positive solutions for nonlinear Robin problems

Date

2017-09-06

Authors

Averna, Diego
Papageorgiou, Nikolaos S.
Tornatore, Elisabetta

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We consider a parametric Robin problem driven by the p-Laplacian with an indefinite potential and with a superlinear reaction term which does not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions. We prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies. We also show the existence of a minimal positive solution ũλ and establish the monotonicity and continuity of the map λ → ũλ.

Description

Keywords

Robin boundary condition, Superlinear reaction, Truncation and comparison techniques, Bifurcation-type result, Minimax positive solution

Citation

Averna, D., Papageorgiou, N. S., & Tornatore, E. (2017). Positive solutions for nonlinear Robin problems. <i>Electronic Journal of Differential Equations, 2017</i>(204), pp. 1-25.

Rights

Attribution 4.0 International

Rights Holder

Rights License