Oscillatory and asymptotic properties of a class of operator-differential inequalities

1984 ◽  
Vol 96 (1-2) ◽  
pp. 5-13 ◽  
Author(s):  
A. D. Myshkis ◽  
D. D. Bainov ◽  
A. I. Zahariev
Keyword(s):  
Asymptotic Behaviour ◽  
Asymptotic Properties ◽  
Neutral Type ◽  
Differential Inequalities ◽  
Functional Differential ◽  
Image Position ◽  
Oscillatory Properties

SynopsisThe present paper studies some asymptotic (including oscillatory) properties of the solutions of operator-differential inequalities of the formwhere(the latter symbol denotes the space of locally summable functions).As an application of the results obtained, theorems are proved for the asymptotic behaviour of the solutions of certain classes of functional-differential and integro-differential neutral-type equations.

scholarly journals Oscillatory properties of the solutions of linear equations of neutral type

1988 ◽  
Vol 38 (2) ◽  
pp. 255-261 ◽  
Author(s):  
D.D. Bainov ◽  
A.D. Myshkis ◽  
A.I. Zahariev
Keyword(s):  
Linear Equations ◽  
Asymptotic Properties ◽  
Neutral Type ◽  
Image Position ◽  
Oscillatory Properties

In this paper the oscillatory and asymptotic properties of solutions of the equationare investigated where δ = ±1, τ > 0, σ > 0, the functions r(s) and are non- decreasing and .

scholarly journals Oscillating properties of the solutions of a class of neutral type functional differential equations

1980 ◽  
Vol 22 (3) ◽  
pp. 365-372 ◽  
Author(s):  
A.I. Zahariev ◽  
D.D. Bainov
Keyword(s):  
Differential Equations ◽  
Positive Constant ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Constant Delay ◽  
Arbitrary Positive Constant ◽  
Functional Differential ◽  
Image Position

The present paper deals with some oscillating and asymptotic properties of the functional differential equations of the formwhere λ is an arbitrary positive constant and τ > 0 is a constant delay.

scholarly journals On Asymptotic Behaviour of Solutions ton-Dimensional Systems of Neutral Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
H. Šamajová ◽  
E. Špániková
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
Asymptotic Behaviour Of Solutions ◽  
Functional Differential Systems ◽  
Functional Differential

This paper presents the properties and behaviour of solutions to a class ofn-dimensional functional differential systems of neutral type. Sufficient conditions for solutions to be either oscillatory, orlimt→∞yi(t)= 0, orlimt→∞|yi(t)|=∞,i=1,2,…,n, are established. One example is given.

13.—The Functional Differential Equation y′(x) = ay(λx) + by(x)

1976 ◽  
Vol 74 ◽  
pp. 165-174 ◽  
Author(s):  
Jack Carr ◽  
Janet Dyson
Keyword(s):  
Differential Equation ◽  
Asymptotic Behaviour ◽  
Functional Differential Equation ◽  
Complex Constant ◽  
Asymptotic Behaviour Of Solutions ◽  
Functional Differential ◽  
Image Position

SynopsisThe paper discusses the asymptotic behaviour of solutions of the functional differential equationwhere a is a complex constant, 0<λ<1, and b is a constant such that Re b = 0, but b ≠ 0.

Existence and properties of semi-bounded global solutions to the functional differential equation with Volterra-type operators on the real line

2017 ◽  
Vol 147 (6) ◽  
pp. 1119-1168
Author(s):  
Maitere Aguerrea ◽  
Robert Hakl
Keyword(s):  
Real Line ◽  
Asymptotic Properties ◽  
Global Solutions ◽  
Continuous Operator ◽  
Volterra Type ◽  
Existence Of A Solution ◽  
Carathéodory Conditions ◽  
Functional Differential ◽  
Image Position ◽  
Continuous Operators

Consider the equationwhere are linear positive continuous operators and f : Cloc(ℝ;ℝ) → Lloc(ℝ;ℝ) is a continuous operator satisfying the local Carathéodory conditions. Efficient conditions guaranteeing the existence of a global solution, which is bounded and non-negative in the neighbourhood of –∞, to the equation considered are established provided that ℓ0, ℓ1 and f are Volterra-type operators. The existence of a solution that is positive on the whole real line is discussed as well. Furthermore, the asymptotic properties of such solutions are studied in the neighbourhood of –∞. The results are applied to certain models appearing in the natural sciences.

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.

Sign in / Sign up

Export Citation Format

Share Document