Nodal solutions for the Robin p-Laplacian plus an indefinite potential and a general reaction term

Nikolaos S. Papageorgiou; Vicenţiu D. Rǎdulescu; Dušan D. Repovš

doi:10.3934/cpaa.2018014

Article Contents

2018, Volume 17, Issue 1: 231-241. Doi: 10.3934/cpaa.2018014

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Nodal solutions for the Robin p-Laplacian plus an indefinite potential and a general reaction term

1.
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
2.
Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3.
Department of Mathematics, University of Craiova, 200585 Craiova, Romania
4.
Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia

* Corresponding author:Vicenţiu D. Rǎdulescu
* Corresponding author:Vicenţiu D. Rǎdulescu

Received: March 31, 2017

Revised: May 31, 2017

Published: December 2017

This research was supported by the Slovenian Research Agency grants P1-0292, J1-8131, J1-7025. V.D. Rǎdulescu acknowledges the support through 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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Abstract

We consider a nonlinear Robin problem driven by the p-Laplacian plus an indefinite potential. The reaction term is of arbitrary growth and only conditions near zero are imposed. Using critical point theory together with suitable truncation and perturbation techniques and comparison principles, we show that the problem admits a sequence of distinct smooth nodal solutions converging to zero in $C^1(\overline{Ω})$ .

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Mathematics Subject Classification: Primary:35J20;Secondary:35J60, 58E05.

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References

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