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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Atypicality of power-law solutions to Emden–Fowler type higher order equations
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by I. V. Astashova
Translated by: I. V. Astashova
St. Petersburg Math. J. 31 (2020), 297-311
DOI: https://doi.org/10.1090/spmj/1597
Published electronically: February 4, 2020
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Abstract:

For higher-order Emden–Fowler type equations, conditions on the roots of a certain polynomial related to the equation are obtained that are sufficient to ensure that asymptotically power-law solutions are atypical. Atypicality means that the set of initial data generating such solutions has measure zero. By using those conditions, atypicality of the asymptotically power-law solutions is proved for the equations of order $12$ to $203$ with sufficiently strong nonlinearity. A review of results is given for the asymptotically power-law behavior of blow-up solutions.
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Bibliographic Information
  • I. V. Astashova
  • Affiliation: Lomonosov Moscow State University, Leninskie gory 1, Moscow, 119991, Russia; and Plekhanov Russian University of Economics, Stremyanny lane 36, Moscow 117997, Russia
  • Email: ast.diffiety@gmail.com
  • Received by editor(s): November 27, 2018
  • Published electronically: February 4, 2020

    • Dedicated: To the 80th anniversary of V. G. Mazya, Master of solving difficult problems
  • © Copyright 2020 American Mathematical Society
  • Journal: St. Petersburg Math. J. 31 (2020), 297-311
  • MSC (2010): Primary 34C11; Secondary 34E05
  • DOI: https://doi.org/10.1090/spmj/1597
  • MathSciNet review: 3937501