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Infinitely many sign-changing solutions for a class of critical elliptic systems with Neumann conditions

Published online by Cambridge University Press:  30 January 2014

D. C. de Morais Filho ,
L. F. O. Faria ,
O. H. Miyagaki  and
F. R. Pereira
D. C. de Morais Filho
Affiliation:
Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Caixa Postal 10044, CEP 58429-970, Campina Grande, Paraíba, Brazil (daniel@dme.ufcg.edu.br)
L. F. O. Faria
Affiliation:
Departamento de Matemática – ICE, Universidade Federal de Juiz de Fora, CEP 36036-330, Juiz de Fora, Minas Gerais, Brazil (luiz.faria@ufjf.edu.br; ohmiyagaki@gmail.com; fabio.pereira@ufjf.edu.br)
O. H. Miyagaki
Affiliation:
Departamento de Matemática – ICE, Universidade Federal de Juiz de Fora, CEP 36036-330, Juiz de Fora, Minas Gerais, Brazil (luiz.faria@ufjf.edu.br; ohmiyagaki@gmail.com; fabio.pereira@ufjf.edu.br)
F. R. Pereira
Affiliation:
Departamento de Matemática – ICE, Universidade Federal de Juiz de Fora, CEP 36036-330, Juiz de Fora, Minas Gerais, Brazil (luiz.faria@ufjf.edu.br; ohmiyagaki@gmail.com; fabio.pereira@ufjf.edu.br)
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Abstract

In this work we study the multiplicity results for a class of critical elliptic systems related to the Brézis–Nirenberg problem with the Neumann boundary condition on a ball. Our approach relies on a minimization argument for an auxiliary problem with a mixed boundary condition and on suitable estimates of the critical level for the system case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 1 , February 2014 , pp. 53 - 69
Copyright
Copyright © Royal Society of Edinburgh 2014 

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