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Soliton solutions to systems of coupled Schrödinger equations of Hamiltonian type


Authors: Boyan Sirakov and Sérgio H. M. Soares
Journal: Trans. Amer. Math. Soc. 362 (2010), 5729-5744
MSC (2010): Primary 35J47, 35J50, 35J10
DOI: https://doi.org/10.1090/S0002-9947-2010-04982-7
Published electronically: May 27, 2010
MathSciNet review: 2661494
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Abstract: We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.


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Additional Information

Boyan Sirakov
Affiliation: UFR SEGMI, Université Paris 10, 92001 Nanterre Cedex, France – and – CAMS, Ecole des Hautes Etudes en Sciences Sociales, 54 bd Raspail, 75270 Paris Cedex 06, France
Email: sirakov@ehess.fr

Sérgio H. M. Soares
Affiliation: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 13560-970, São Carlos-SP, Brazil
Email: monari@icmc.usp.br

DOI: https://doi.org/10.1090/S0002-9947-2010-04982-7
Received by editor(s): May 28, 2008
Published electronically: May 27, 2010
Additional Notes: The second author’s research was supported in part by FAPESP
Article copyright: © Copyright 2010 American Mathematical Society

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