CLASSIFICATION AND EXISTENCE OF POSITIVE
SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDING ON THE UNKNOWN FUNCTION

数学物理学报(英文版) ›› 2004, Vol. 24 ›› Issue (3): 403-411.

CLASSIFICATION AND EXISTENCE OF POSITIVE
SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDING ON THE UNKNOWN FUNCTION

李万同,董仲奇

Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, China

出版日期:2004-07-20 发布日期:2004-07-20
基金资助:
Supported by the NNSF of China (10171040), the NSF
of Gansu Province of China (ZS011-A25-007-Z), the Foundation for University Key Teacher by Ministry of
Education of China, and the Teaching and Research Award Program for Outstanding Young Teachers in Higher
Education Institutions of Ministry of Education of China.

CLASSIFICATION AND EXISTENCE OF POSITIVE
SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDING ON THE UNKNOWN FUNCTION

LI Mo-Tong, DONG Zhong-Ai

Online:2004-07-20 Published:2004-07-20
Supported by:
Supported by the NNSF of China (10171040), the NSF
of Gansu Province of China (ZS011-A25-007-Z), the Foundation for University Key Teacher by Ministry of
Education of China, and the Teaching and Research Award Program for Outstanding Young Teachers in Higher
Education Institutions of Ministry of Education of China.

摘要/Abstract

摘要：

A class of second order nonlinear differential equations with delay depenging
on the unknown function of the from
??r(t)'(x(t))x′(t)′
+ f (t, x(t), x ((t, x(t)))) = 0
in the case where R ∞
0 ds/r(s) < 1 is studied. Various classifications of their eventually
positive solutions are given in terms of their asymptotic magnitudes, and necessary as well
as sufficient conditions for the existence of these solutions are also obtained.

Abstract:

Key words: Nonlinear differential equation with delay, eventually positive solution;as-
ymptotic behavior;fixed point theorem

中图分类号:

34K15

李万同, 董仲奇. CLASSIFICATION AND EXISTENCE OF POSITIVE
SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDING ON THE UNKNOWN FUNCTION[J]. 数学物理学报(英文版), 2004, 24(3): 403-411.

LI Mo-Tong, DONG Zhong-Ai. CLASSIFICATION AND EXISTENCE OF POSITIVE
SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDING ON THE UNKNOWN FUNCTION[J]. Acta mathematica scientia,Series B, 2004, 24(3): 403-411.

CLASSIFICATION AND EXISTENCE OF POSITIVE
SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDING ON THE UNKNOWN FUNCTION

CLASSIFICATION AND EXISTENCE OF POSITIVE
SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDING ON THE UNKNOWN FUNCTION

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CLASSIFICATION AND EXISTENCE OF POSITIVE SOLUTIONS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAY DEPENDING ON THE UNKNOWN FUNCTION

CLASSIFICATION AND EXISTENCE OF POSITIVE SOLUTIONS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAY DEPENDING ON THE UNKNOWN FUNCTION

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CLASSIFICATION AND EXISTENCE OF POSITIVE
SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDING ON THE UNKNOWN FUNCTION

CLASSIFICATION AND EXISTENCE OF POSITIVE
SOLUTIONS OF SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDING ON THE UNKNOWN FUNCTION