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
and establish the monotonicity and
continuity of the map
.
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.
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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 |
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