Nikolaos Socrates Papageorgiou (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (Author)

Abstract

We study a parametric Robin problem driven by a nonlinear nonhomogeneous differential operator and with a superlinear Carathéodory reaction term. We prove a bifurcation-type theorem for small values of the parameter. Also, we show that as the parameter ▫$\lambda > 0$▫ approaches zero, we can find positive solutions with arbitrarily big and arbitrarily small Sobolev norm. Finally, we show that for every admissible parameter value, there is a smallest positive solution ▫$u^\ast_\lambda$▫ of the problem, and we investigate the properties of the map ▫$\lambda \mapsto u^\ast_\lambda$▫.

Keywords

Robin boundary condition;nonlinear nonhomogeneous differential operator;nonlinear regularity;nonlinear maximum principle;bifurcation-type result;extremal positive solution;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 517.956.2
COBISS: 18103641 Link will open in a new window
ISSN: 0933-7741
Views: 539
Downloads: 316
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Other data

Type (COBISS): Article
Pages: str. 553-580
Volume: ǂVol. ǂ30
Issue: ǂiss. ǂ3
Chronology: May 2018
DOI: 10.1515/forum-2017-0124
ID: 11207985