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. Electronic Journal of Differential Equations, 2017(204), pp. 1-25.
Rights
Attribution 4.0 International