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

  • Yu. N. DrozhzhinovEmail author
  • B. I. Zavialov
Article
  • 32 Downloads

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.

Keywords

Generalize Function STEKLOV Institute Homogeneous Polynomial Tauberian Theorem Positive Continuous Function 
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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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