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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 053, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.053 (Mi sigma179) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Lie Symmetries and Criticality of Semilinear Differential Systems

Yuri Bozhkova, Enzo Mitidierib

a Departamento de Matemática Aplicada, Instituto de Matemática, Estatistica e Computação Científica, Universidade Estadual de Campinas - UNICAMP, C.P. 6065, 13083-970 - Campinas - SP, Brasil
b Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via Valerio 12/1, 34127 Trieste, Italia
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DOI: https://doi.org/10.3842/SIGMA.2007.053
Abstract: We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers.
Keywords: Pokhozhaev identities; Noether identity; critical exponents.
Received: February 1, 2007; in final form March 20, 2007; Published online March 25, 2007
Bibliographic databases:
Document Type: Article
MSC: 35J50; 35J20; 35J60; 35L70
Language: English
Citation: Yuri Bozhkov, Enzo Mitidieri, “Lie Symmetries and Criticality of Semilinear Differential Systems”, SIGMA, 3 (2007), 053, 17 pp.
Citation in format AMSBIB
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\by Yuri Bozhkov, Enzo Mitidieri
\paper Lie Symmetries and Criticality of Semilinear Differential Systems
\jour SIGMA
\yr 2007
\vol 3
\papernumber 053
\totalpages 17
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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