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

被引：0

作者：

Filimonova I.V. ^{[1
]}

Khachlaev T.S. ^{[2
]}

机构：

[1] Lomonosov Moscow State University, GSP-1 Leninskie Gory 1, Moscow

[2] Moscow Technological University, pr. Vernadskogo 78, Moscow

来源：

Russian Mathematics | 2017年 / 61卷 / 3期

关键词：

asymptotic behavior of solutions; Emden–Fowler equation; existence of solution; maximum principle; nonlinear equation; ordinary differential equation; positive solution; semilinear equation;

D O I：

10.3103/S1066369X17030069

中图分类号：

学科分类号：

摘要：

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. © 2017, Allerton Press, Inc.

引用

页码：49 / 57

页数：8

共 9 条

[1]

Bellman R., Stability Theory of Differential Equations, (1954)

[2]

Kiguradze I.T., Asymptotische Eigenschaften der Lösungen einer nichtlinearen Differentialgleichung von Emden–Fowlerschem Typ, Izv. Akad. Nauk SSSR, Ser. Mat., 29, pp. 965-986, (1965)

[3]

Khachlaev T.S., The Asymptotic Behaviour of Solutions of a Semilinear Elliptic Equation with Increasing Coefficient in a Cylindrical Domain, Russian Math. Surveys, 59, 2, pp. 383-384, (2004)

[4]

Astashova I., On Asymptotic Behavior of Solutions to a Quasi-Linear SecondOrder Differential Equations, Funct. Diff. Equat., 16, 1, pp. 93-115, (2009)

[5]

Surnachev M.D., On Asymptotic Behavior of Positive Solutions to Emden–Fowler Type Equations, J. Math. Sci., New York, 177, 1, pp. 148-207, (2011)

[6]

Surnachev M.D., Estimates for Emden–Fowler Type Inequalities with Absorption Term, J. Math. Anal. Appl., 348, 2, pp. 996-1011, (2008)

[7]

Filimonova I.V., On the Behavior of Solutions of a Semilinear Parabolic or Elliptic Equation Satisfying a Nonlinear Boundary Condition in Cylindrical Domain, J. Math. Sciences, 143, 4, pp. 3415-3428, (2007)

[8]

Mirazai A.A., On Behaviour of Solutions toWeak Nonlinear SecondOrder Elliptic Equations in Unbounded Domains, Vestnik MSU, Ser. 1, Math. Mekh., No., 4, pp. 6-8, (1994)

[9]

Atkinson F.V., On Second Order Nonlinear Oscillations, Pacif. J.Math. 5, Suppl., 1, pp. 643-647, (1955)

← 1 →