Positive solutions for nonlinear nonhomogeneous parametric Robin problems
ID Papageorgiou, Nikolaos S. (Author), ID Rǎdulescu, Vicenţiu (Author), ID Repovš, Dušan (Author)

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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
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Number of pages:Str. 553-580
Numbering:Vol. 30, iss. 3
PID:20.500.12556/RUL-109200 This link opens in a new window
ISSN on article:0933-7741
DOI:10.1515/forum-2017-0124 This link opens in a new window
COBISS.SI-ID:18103641 This link opens in a new window
Publication date in RUL:26.08.2019
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Title:Forum mathematicum
Shortened title:Forum math.
Publisher:de Gruyter
COBISS.SI-ID:26801408 This link opens in a new window

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