华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 6: 94 - 101

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.06.010

数学

非线性常微分方程的解在无穷处的渐近行为

  • SERGEY Prokhozhiy ,
  • 倪明康
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  • 1. 维特伯斯克州立大学 数学系, 维特伯斯克 210038, 白俄罗斯;
    2. 华东师范大学 数学系, 上海 200241

收稿日期: 2015-12-03

  网络出版日期: 2017-01-13

基金资助

国家自然科学基金(11471118, 30921064, 90820307); 中科院创新项目; 上海PMMP重点实验室

收起

On the asymptotic behavior of solutions of nonlinear ordinary differential equations

  • SERGEY Prokhozhiy ,
  • NI Ming-kang
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  • 1. The Faculty of Mathematics, Vitebsk State University, Vitebsk 210038, Belarus;
    2. Department of Mathematics, East China Normal University, Shanghai 200241, China

Received date: 2015-12-03

  Online published: 2017-01-13

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摘要

本文研究了非线性常微分方程v''-c1(vn)'-c2vp=0解的渐近行为. 考虑了所有参数间的相互关系. 确立了第一渐近项以及在第二渐近项下存在的诸多情形. 同时研究了正负值下的柯西问题.

关键词： 常微分方程; 渐近行为; 非线性

本文引用格式

SERGEY Prokhozhiy , 倪明康 . 非线性常微分方程的解在无穷处的渐近行为[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(6) : 94 -101 . DOI: 10.3969/j.issn.1000-5641.2016.06.010

Abstract

In this paper we investigate the asymptotic behavior of solutions of the Cauchy problem for nonlinear ordinary differential equation v''-c1(vn)'-c2vp=0. All interrelations of parameters are considered. The first asymptotic term and in a number of cases the second asymptotic term is found. The Cauchy problem is investigated both for positive and negative values of argument.

Key words： ordinary differential equations; asymptotic behavior; nonlinear

参考文献

[ 1 ] GLADKOV A L. Stationary solutions of some quasilinear parabolic equations [J]. Journal of Vitebsk State University, 1997(1): 56-61.
[ 2 ] TERSENOV A S. The Cauchy problem for a class of quasilinear parabolic equations [J]. Annali Di Matematica Pura Ed Applicata, 2003, 182(3): 325-336.
[ 3 ] ZAKHAROV S V. The Cauchy problem for a quasilinear parabolic equation with two small parameters [J]. Doklady Mathematics, 2008, 78(78): 769-770.
[ 4 ] BABKIN B N. The theorem of S A Chaplygin on differential inequalities [J]. Diseases of Aquatic Organisms, 2000, 41(2): 151-158.
[ 5 ] GLADKOV A L. The Cauchy problem in classes of increasing functions for the equation of filtration with convection [J]. Sbornik Mathematics, 1995, 186(6): 35-56.

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