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On Asymptotic Classification of Solutions to Nonlinear Regular and Singular Third- and Fourth-Order Differential Equations with Power Nonlinearity

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Differential and Difference Equations with Applications (ICDDEA 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 164))

Abstract

For the equation

$$\displaystyle{ y^{(n)} + p_{ 0}\,\vert y\vert ^{k}\ \mathrm{sign}\,y = 0, }$$

in the cases n = 3, 4, p 0 > 0 or p 0 < 0 for regular nonlinearity k > 1 and singular nonlinearity 0 < k < 1 asymptotic classification of all solutions are given.

It is the first time when all results on this classification are represented together for regular and singular cases.

UDK 517.91

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory, GSP-1, 119991, Moscow, Russia

    I. V. Astashova

Authors
  1. I. V. Astashova
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Correspondence to I. V. Astashova .

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Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Zuzana Došlá

  3. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Ondřej Došlý

  4. School of Mathematics and Stastistics, Huazhong University of Science and Technology, Wuhan, China

    Peter E. Kloeden

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Astashova, I.V. (2016). On Asymptotic Classification of Solutions to Nonlinear Regular and Singular Third- and Fourth-Order Differential Equations with Power Nonlinearity. In: Pinelas, S., Došlá, Z., Došlý, O., Kloeden, P. (eds) Differential and Difference Equations with Applications. ICDDEA 2015. Springer Proceedings in Mathematics & Statistics, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-319-32857-7_18

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