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 Tr. Mat. Inst. Steklova, 2014, Volume 285, Pages 107–127 (Mi tm3554)

Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter group

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We study solutions to partial differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter transformation group such that all eigenvalues of the infinitesimal matrix are positive. The infinitesimal matrix may contain a nilpotent part. In the asymptotic scale of regularly varying functions, we find conditions under which such differential equations have asymptotically homogeneous solutions in the critical case.

 Funding Agency Grant Number Russian Foundation for Basic Research 13-01-00065 Ministry of Education and Science of the Russian Federation NSh-864.2014.1 This work was supported in part by the Russian Foundation for Basic Research (project no. 13-01-00065) and by a grant of the President of the Russian Federation (project no. NSh-864.2014.1).

DOI: https://doi.org/10.1134/S0371968514020083

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 285, 99–119

Bibliographic databases:

Document Type: Article
UDC: 517.5

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter group”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Tr. Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 107–127; Proc. Steklov Inst. Math., 285 (2014), 99–119

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3554
• https://doi.org/10.1134/S0371968514020083
• http://mi.mathnet.ru/eng/tm/v285/p107

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This publication is cited in the following articles:
1. Yu. N. Drozhzhinov, “Asymptotically homogeneous generalized functions and some of their applications”, Proc. Steklov Inst. Math., 301 (2018), 65–81
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