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Multiplicity of solutions for nonlinear nonhomogeneous Robin problems


Authors: Nikolaos S. Papageorgiou and Vicenţiu D. Rădulescu
Journal: Proc. Amer. Math. Soc. 146 (2018), 601-611
MSC (2010): Primary 35J20; Secondary 35J60
DOI: https://doi.org/10.1090/proc/13862
Published electronically: September 13, 2017
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Abstract: We consider a nonlinear nonhomogeneous Robin problem, with an indefinite concave term near the origin and a perturbation of arbitrary growth. By modifying the perturbation and using a variant of the symmetric mountain pass theorem due to Heinz (J. Diff. Equ. 66 (1987)), we show that the problem has a whole sequence of distinct nontrivial smooth solutions converging to the trivial solution.


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Nikolaos S. Papageorgiou
Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
Email: npapg@math.ntua.gr

Vicenţiu D. Rădulescu
Affiliation: Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia – and – Department of Mathematics, University of Craiova, Street A.I. Cuza 13, 200585 Craiova, Romania
Email: vicentiu.radulescu@imar.ro

DOI: https://doi.org/10.1090/proc/13862
Keywords: Robin boundary condition, nonhomogeneous differential operator, indefinite concave term, nonlinear regularity theory, infinitely many solutions
Received by editor(s): July 13, 2016
Received by editor(s) in revised form: March 13, 2017
Published electronically: September 13, 2017
Additional Notes: The second author acknowledges the support through a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, project number PN-III-P4-ID-PCE-2016-0130.
Communicated by: Catherine Sulem
Article copyright: © Copyright 2017 American Mathematical Society

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