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Differential Equations

, Volume 55, Issue 5, pp 581–590 | Cite as

Asymptotic Behavior of Singular Solutions of Emden-Fowler Type Equations

  • I. V. AstashovaEmail author
Ordinary Differential Equations
  • 8 Downloads

Abstract

We study the behavior of singular solutions of the Emden-Fowler type equation y(n) = p(x, y, y’,..., y(n-1)|y|k sgn y, n > 2, with a regular (k > 1) or singular (0 < k < 1) nonlinearity. A singular solution is a solution that has a vertical (possibly, resonance) asymptote (for k > 1) or a solution that vanishes together with derivatives of order < n at some point or has a point of accumulation of zeros (for 0 < k < 1).

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Plekhanov Russian University of EconomicsMoscowRussia

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