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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
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
Citation:
Yuri Bozhkov, Enzo Mitidieri, “Lie Symmetries and Criticality of Semilinear Differential Systems”, SIGMA, 3 (2007), 053, 17 pp.
Linking options:
https://www.mathnet.ru/eng/sigma179 https://www.mathnet.ru/eng/sigma/v3/p53
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Abstract page: | 258 | Full-text PDF : | 71 | References: | 36 |
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