Electron. J. Differential Equations, Vol. 2017 (2017), No. 204, pp. 1-25.

Positive solutions for nonlinear Robin problems

Diego Averna, Nikolaos S. Papageorgiou, Elisabetta Tornatore

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 $\tilde{u}_\lambda$ and establish the monotonicity and continuity of the map $\lambda\to \tilde{u}_\lambda$.

Submitted June 7, 2017. Published September 6, 2017.
Math Subject Classifications: 35J25, 35J80
Key Words: Robin boundary condition; superlinear reaction; truncation and comparison techniques; bifurcation-type result; minimax positive solution.

Show me the PDF file (350 KB), TEX file for this article.

Diego Averna
Dipartimento di Matematica e Informatica
Università degli studi di Palermo
Via Archirafi, 90123 - Palermo, Italy
email: diego.averna@unipa.it
  Nikolaos S. Papageorgiou
Department of Mathematics
National Technical University
Zografou Campus, Athens 15780, Greece
email: npapg@math.ntua.gr
Elisabetta Tornatore
Dipartimento di Matematica e Informatica
Università degli studi di Palermo
Via Archirafi, 90123 Palermo, Italy
email: elisa.tornatore@unipa.it

Return to the EJDE web page