This article is cited in 1 paper

On asymptotic properties of solutions defined on a half-axis to one semilinear ordinary differential equation

I. V. Filimonova^a, T. S. Khachlaev<sup>b

a</sup> Lomonosov Moscow State University, GSP-1 Leninskie Gory, Moscow, 119991 Russia
^b Moscow Technological University, 78 Vernadskogo Аve., Moscow, 119454 Russia

Abstract: We consider solutions to the semilinear ordinary differential equation with a nonlinear term of Emden–Fowler type. The results about the asymptotic behavior of the solutions to the Emden–Fowler equation defined in a neighborhood of infinity, presented in the book of R. Bellman, are extended to the case of equation with lower-order derivative.

Keywords: ordinary differential equation, nonlinear equation, semilinear equation, Emden–Fowler equation, asymptotic behavior of solutions, positive solution, existence of solution, maximum principle.

UDC: 517.923

Received: 17.09.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:3, 49–57

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