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

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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 ▫$\lambda \mapsto u^\ast_\lambda$▫.

Language:English
Keywords:Robin boundary condition, nonlinear nonhomogeneous differential operator, nonlinear regularity, nonlinear maximum principle, bifurcation-type result, extremal positive solution
Work type:Article (dk_c)
Tipology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
Year:2018
Number of pages:str. 553-580
Numbering:Vol. 30, iss. 3
UDC:517.956.2
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
Views:284
Downloads:197
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Record is a part of a journal

Title:Forum mathematicum
Shortened title:Forum math.
Publisher:de Gruyter
ISSN:0933-7741
COBISS.SI-ID:26801408 This link opens in a new window

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