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Licensed Unlicensed Requires Authentication Published by De Gruyter August 15, 2017

Positive solutions for nonlinear nonhomogeneous parametric Robin problems

  • Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu ORCID logo EMAIL logo and Dušan D. Repovš
From the journal Forum Mathematicum

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 λ>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 uλ* of the problem, and we investigate the properties of the map λuλ*.

MSC 2010: 35J20; 35J60

Communicated by Christopher D. Sogge


Award Identifier / Grant number: P1-0292

Award Identifier / Grant number: J1-8131

Award Identifier / Grant number: J1-7025

Funding statement: This research was supported by the Slovenian Research Agency grants P1-0292, J1-8131, J1-7025. V. D. Rădulescu was also supported by a grant of Ministry of Research and Innovation, CNCS-UEFISCDI, project number PN-III-P4-ID-PCE-2016-0130, within PNCDI III.

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Received: 2017-6-12
Revised: 2017-7-13
Published Online: 2017-8-15
Published in Print: 2018-5-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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