Asymptotic behaviour of functional-differential equations with proportional time delays

This paper discusses the initial value problem where A, B i and C i are d × d complex matrices, p i , q i ∈ (0, 1), i = 1, 2, …, and y 0 is a column vector in ℂ d . 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.

[1]  Yunkang Li,et al.  Stability analysis of $\theta$ -methods for neutral functional-differential equations , 1995 .

[2]  Arieh Iserles,et al.  On Neutral Functional)Differential Equations with Proportional Delays , 1997 .

[3]  Arieh Iserles,et al.  On the generalized pantograph functional-differential equation , 1993, European Journal of Applied Mathematics.

[4]  Klaus Schmitt,et al.  Delay and functional differential equations and their applications : [proceedings] , 1972 .

[5]  John Ockendon,et al.  The dynamics of a current collection system for an electric locomotive , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[6]  Gregory Derfel.  Behavior of solutions of functional and differential-functional equations with several transformations of the independent variable , 1982 .

[7]  J. B. McLeod,et al.  The functional-differential equation $y'\left( x \right) = ay\left( {\lambda x} \right) + by\left( x \right)$ , 1971 .

[8]  The Difference-Differential Equation F'(x) = eαx+β F(x–1) I , 1953 .

[9]  G. Derfel,et al.  Kato Problem for Functional-Differential Equations and Difference Schrödinger Operators , 1990 .

[10]  Alan Feldstein,et al.  THE PHRAGMÉN-LINDELÖF PRINCIPLE AND A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS , 1972 .

[11]  Y. Katznelson.  An Introduction to Harmonic Analysis: Interpolation of Linear Operators , 1968 .

[12]  Arieh Iserles,et al.  On nonlinear delay differential equations , 1994 .

[13]  Y. Kuang,et al.  Monotonic and oscillatory solutions of a linear neutral delay equation with infinite lag , 1990 .

[14]  L. Fox,et al.  On a Functional Differential Equation , 1971 .

[15]  P. Hartman.  Ordinary Differential Equations , 1965 .

[16]  Arieh Iserles,et al.  On Pantograph Integro-Differential Equations , 1994 .

[17]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[18]  Z. Jackiewicz,et al.  Unstable Neutral Fuctional Differential Equations , 1990, Canadian Mathematical Bulletin.

[19]  Jack Carr,et al.  13.—The Functional Differential Equation y′(x) = ay(λx) + by(x) , 1976, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[20]  J. Carr,et al.  2.—The Matrix Functional Differential Equation y′(x) = Ay(λx) + By(x) , 1976, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.