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On branches of positive solutions for $ p$-Laplacian problems at the extreme value of the Nehari manifold method


Authors: Yavdat Ilyasov and Kaye Silva
Journal: Proc. Amer. Math. Soc. 146 (2018), 2925-2935
MSC (2010): Primary 35J61, 35J92, 35J50
DOI: https://doi.org/10.1090/proc/13972
Published electronically: March 14, 2018
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Abstract: This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the
$ p$-Laplacian, an indefinite nonlinearity, and depend on a real parameter $ \lambda $. A special focus is given to the extreme value $ \lambda ^*$ of the Nehari manifold that determines the threshold of applicability of the Nehari manifold method. In the main result the existence of two branches of positive solutions for the cases where the parameter $ \lambda $ lies above the threshold $ \lambda ^*$ is obtained.


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Additional Information

Yavdat Ilyasov
Affiliation: Institute of Mathematics, Ufa Scientific Centre, Russian Academy of Sciences, Chenryshevsky str. 112, 450008, Ufa, Russia
Email: ilyasov02@gmail.com

Kaye Silva
Affiliation: Instituto de Matemática e Estatística
Address at time of publication: Universidade Federal de Goiás, Campus II, CEP 74690-900 Goiânia, Brazil
Email: kayeoliveira@hotmail.com

DOI: https://doi.org/10.1090/proc/13972
Received by editor(s): April 18, 2017
Received by editor(s) in revised form: September 13, 2017
Published electronically: March 14, 2018
Communicated by: Catherine Sulem
Article copyright: © Copyright 2018 American Mathematical Society

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