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Nodal Solutions for Nonlinear Non-Homogeneous Robin Problems with an Indefinite Potential

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  13 June 2018

Leszek Gasiński  and
Nikolaos S. Papageorgiou
Leszek Gasiński*
Affiliation:
Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland (Leszek.Gasinski@ii.uj.edu.pl)
Nikolaos S. Papageorgiou
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece (npapg@math.ntua.gr)
*
*Corresponding author.
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Abstract

We consider a nonlinear Robin problem driven by a non-homogeneous differential operator plus an indefinite potential term. The reaction function is Carathéodory with arbitrary growth near±∞. We assume that it is odd and exhibits a concave term near zero. Using a variant of the symmetric mountain pass theorem, we establish the existence of a sequence of distinct nodal solutions which converge to zero.

Keywords

Robin boundary conditionnonlinear non-homogeneous differential operatornonlinear regularity theorynodal solutions

MSC classification

Primary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 943 - 959
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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