Positive solutions for nonlinear nonhomogeneous parametric Robin problems
Papageorgiou, Nikolaos (Author), Rǎdulescu, Vicenţiu (Author), Repovš, Dušan (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 ▫$\lambda \mapsto u^\ast_\lambda$▫.

Language: English Robin boundary condition, nonlinear nonhomogeneous differential operator, nonlinear regularity, nonlinear maximum principle, bifurcation-type result, extremal positive solution Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of Education 2018 str. 553-580 Vol. 30, iss. 3 517.956.2 0933-7741 10.1515/forum-2017-0124 18103641 284 197 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

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Title: Forum mathematicum Forum math. de Gruyter 0933-7741 26801408