arXiv math-ph/07030712007-03-25math-phmath.APmath.MPnlin.SI

Lie Symmetries and Criticality of Semilinear Differential Systems

Yuri Bozhkov, Enzo Mitidieri

备注：: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
发表信息：: SIGMA 3 (2007), 053, 17 pages
DOI：: 10.3842/SIGMA.2007.053

英文摘要：

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.

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