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On the existence of infinite energy solutions for nonlinear Schrödinger equations


Authors: Pablo Braz e Silva, Lucas C. F. Ferreira and Elder J. Villamizar-Roa
Journal: Proc. Amer. Math. Soc. 137 (2009), 1977-1987
MSC (2000): Primary 35Q55, 35D05, 35B40
DOI: https://doi.org/10.1090/S0002-9939-09-09773-1
Published electronically: January 21, 2009
MathSciNet review: 2480279
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Abstract | References | Similar Articles | Additional Information

Abstract: We derive new results about existence and uniqueness of local and global solutions for the nonlinear Schrödinger equation, including self-similar solutions. Our analysis is performed in the framework of weak-$ L^{p}$ spaces.


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Additional Information

Pablo Braz e Silva
Affiliation: Departamento de Matemática, Universidade Federal de Pernambuco, 50740-540, Recife, PE, Brazil
Email: pablo@dmat.ufpe.br

Lucas C. F. Ferreira
Affiliation: Departamento de Matemática, Universidade Federal de Pernambuco, 50740-540, Recife, PE, Brazil
Email: lcff@dmat.ufpe.br

Elder J. Villamizar-Roa
Affiliation: Escuela de Matemáticas, Universidad Industrial de Santander, A.A. 678, Bucaramanga, Colombia
Email: jvillami@uis.edu.co

DOI: https://doi.org/10.1090/S0002-9939-09-09773-1
Received by editor(s): December 12, 2007
Published electronically: January 21, 2009
Additional Notes: The first author was partly supported during this work by CAPES/MECD-DGU Brazil/Spain, grant No. 117/06.
Communicated by: Hart F. Smith
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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