Journal
FORUM MATHEMATICUM
Volume 30, Issue 3, Pages 553-580Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/forum-2017-0124
Keywords
Robin boundary condition; nonlinear nonhomogeneous differential operator; nonlinear regularity; nonlinear maximum principle; bifurcation-type result; extremal positive solution
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Funding
- Slovenian Research Agency [P1-0292, J1-8131, J1-7025]
- Ministry of Research and Innovation, CNCS-UEFISCDI, within PNCDI III [PN-III-P4-ID-PCE-2016-0130]
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We study a parametric Robin problem driven by a nonlinear nonhomogeneous differential operator and with a superlinear Caratheodory 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*(A) of the problem, and we investigate the properties of the map lambda -> u*A.
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