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Lie Symmetries and Criticality of Semilinear Differential Systems

Yuri Bozhkov·Enzo Mitidieri
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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.

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Yuri Bozhkov, Enzo Mitidieri. 2007-03-25. Lie Symmetries and Criticality of Semilinear Differential Systems. https://doi.org/10.3842/sigma.2007.053

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