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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Ground state and non-ground state solutions of some strongly coupled elliptic systems


Authors: Denis Bonheure, Ederson Moreira dos Santos and Miguel Ramos
Journal: Trans. Amer. Math. Soc. 364 (2012), 447-491
MSC (2000): Primary 35J55; Secondary 35J50, 58E05
Published electronically: August 9, 2011
MathSciNet review: 2833588
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Abstract: We study an elliptic system of the form $ Lu = \left\vert v\right\vert^{p-1} v$ and $ Lv=\left\vert u\right\vert^{q-1} u$ in $ \Omega$ with homogeneous Dirichlet boundary condition, where $ Lu:=-\Delta u$ in the case of a bounded domain and $ Lu:=-\Delta u + u$ in the cases of an exterior domain or the whole space $ \mathbb{R}^N$. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.


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Additional Information

Denis Bonheure
Affiliation: Département de Mathématique, Université libre de Bruxelles, CP 214, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
Email: denis.bonheure@ulb.ac.be

Ederson Moreira dos Santos
Affiliation: Instituto de Ciências Matemáticas e de Computaçäo, Universidade de São Paulo, Caixa Postal 668, CEP 13560-970, São Carlos - SP, Brazil
Email: ederson@icmc.usp.br

Miguel Ramos
Affiliation: Faculty of Science, CMAF, University of Lisbon, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
Email: mramos@ptmat.fc.ul.pt

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05452-8
PII: S 0002-9947(2011)05452-8
Keywords: Elliptic system, ground state solution, positive solution, sign changing solution, symmetry
Received by editor(s): October 16, 2009
Received by editor(s) in revised form: August 10, 2010
Published electronically: August 9, 2011
Additional Notes: The first and second authors were partially supported by the bilateral agreement F.R.S.-FNRS & CNPq
The second author was supported by CAPES # 4316/07-0 and FAPESP # 07/54872-8
The third author was supported by FCT, Fundação para a Ciência e a Tecnologia, Financiamento Base 2008 - ISFL/1/209
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.