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Atypicality of power-law solutions to Emden-Fowler type higher order equations


Author: I. V. Astashova
Translated by: I. V. Astashova
Original publication: Algebra i Analiz, tom 31 (2019), nomer 2.
Journal: St. Petersburg Math. J. 31 (2020), 297-311
MSC (2010): Primary 34C11; Secondary 34E05
DOI: https://doi.org/10.1090/spmj/1597
Published electronically: February 4, 2020
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Abstract | References | Similar Articles | Additional Information

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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Additional 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

DOI: https://doi.org/10.1090/spmj/1597
Keywords: Emden--Fowler equation, blow-up solutions, asymptotically power-law solutions
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
Article copyright: © Copyright 2020 American Mathematical Society