Asymptotic Behaviour of Non-Oscillatory Solutions of Functional Differential Equations of Arbitrary Order

1976 ◽  
Vol s2-14 (1) ◽  
pp. 106-112 ◽  
Author(s):  
Takaŝi Kusano ◽  
Hiroshi Onose
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Arbitrary Order ◽  
Functional Differential Equations ◽  
Oscillatory Solutions ◽  
Functional Differential

scholarly journals Nonoscillation theorems for functional differential equations of arbitrary order

1984 ◽  
Vol 7 (2) ◽  
pp. 249-256 ◽  
Author(s):  
John R. Graef ◽  
Myron K. Grammatikopoulos ◽  
Yuichi Kitamura ◽  
Takasi Kusano ◽  
Hiroshi Onose ◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Arbitrary Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Solutions ◽  
Nonlinear Functional ◽  
Functional Differential ◽  
Nonoscillation Theorem

The authors give sufficient conditions for all oscillatory solutions of a sublinear forced higher order nonlinear functional differential equation to converge to zero. They then prove a nonoscillation theorem for such equations. A few intermediate results are also obtained.

Asymptotic behaviour of functional-differential equations with proportional time delays

1996 ◽  
Vol 7 (1) ◽  
pp. 11-30 ◽  
Author(s):  
Yunkang Liu
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Initial Value Problem ◽  
Time Delays ◽  
Functional Differential Equations ◽  
Analytic Solutions ◽  
Comprehensive Analysis ◽  
Initial Value ◽  
Functional Differential ◽  
Image Position

This paper discusses the initial value problemwhereA, BiandCiared × dcomplex matrices,pi,qi∈ (0, 1),i= 1, 2, …, andy0is a column vector in ℂd. By using ideas from the theory of ordinary differential equations and the theory of functional equations, we give a comprehensive analysis of the asymptotic behaviour of analytic solutions of this initial value problem.

scholarly journals Slowly Varying Solutions of Functional Differential Equations with Retarded and Advanced Arguments

2007 ◽  
Vol 14 (2) ◽  
pp. 301-314
Author(s):  
Takaŝi Kusano ◽  
Vojislav Marić
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Functional Differential Equations ◽  
Asymptotic Behaviour Of Solutions ◽  
Functional Differential ◽  
Precise Asymptotic

Abstract Regularity, in the sense of Karamata, (with nonoscillation as a consequence) and the precise asymptotic behaviour of solutions of two functional differential equations are studied.

scholarly journals Asymptotic behaviour of solutions to neutral functional differential equations

1989 ◽  
Vol 40 (3) ◽  
pp. 345-355
Author(s):  
Shaozhu Chen ◽  
Qingguang Huang
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Functional Differential Equation ◽  
Necessary Conditions ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equation ◽  
Neutral Functional Differential Equations ◽  
Functional Differential

Sufficient or necessary conditions are established so that the neutral functional differential equation [x(t) − G(t, xt)]″ + F(t, xt) = 0 has a solution which is asymptotic to a given solution of the related difference equation x(t) = G(t, xt) + a + bt, where a and b are constants.

Sign in / Sign up

Export Citation Format

Share Document