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Existence and multiplicity of solutions for discontinuous elliptic problems in ℝN

Part of: Existence theories Equations and inequalities involving nonlinear operators

Published online by Cambridge University Press:  28 April 2020

Claudianor O. Alves ,
Ziqing Yuan  and
Lihong Huang
Claudianor O. Alves
Affiliation:
Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática, CEP:58429-900 Campina Grande-Pb, Brazil ([email protected])
Ziqing Yuan
Affiliation:
Department of Mathematics, Shaoyang University, Shaoyang, Hunan422000, P.R. China ([email protected])
Lihong Huang
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, Hunan410082, P.R. China ([email protected])
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Abstract

This paper concerns with the existence of multiple solutions for a class of elliptic problems with discontinuous nonlinearity. By using dual variational methods, properties of the Nehari manifolds and Ekeland's variational principle, we show how the ‘shape’ of the graph of the function A affects the number of nontrivial solutions.

Keywords

Multiplicity of solutionsvariational methoddiscontinuous nonlinearity

MSC classification

Secondary: 47J30: Variational methods 49J52: Nonsmooth analysis
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 2 , April 2021 , pp. 548 - 572
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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