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SIGMA 3 (2007), 053, 17 pages math-ph/0703071
https://doi.org/10.3842/SIGMA.2007.053
Lie Symmetries and Criticality of Semilinear Differential Systems
Yuri Bozhkov a and Enzo Mitidieri b
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
Received February 01, 2007, in final form March 20, 2007; Published online March 25, 2007
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.
Key words:
Pokhozhaev identities; Noether identity; critical exponents.
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