On the initial value problem for a class of functional-differential equations

1974 ◽  
Vol 55 (4) ◽  
pp. 275-299 ◽  
Author(s):  
Bernard D. Coleman ◽  
David R. Owen
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Functional Differential

scholarly journals A singular initial value problem for some functional differential equations

2004 ◽  
Vol 2004 (3) ◽  
pp. 261-270 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
Oleksandr E. Zernov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Singular Initial Value Problem ◽  
Functional Differential

For the initial value problem trx′(t)=at+b1x(t)+b2x(q1t)+b3trx′(q2t)+φ(t,x(t),x(q1t),x′(t),x′(q2t)), x(0)=0, where r>1, 0<qi≤1, i∈{1,2}, we find a nonempty set of continuously differentiable solutions x:(0,ρ]→ℝ, each of which possesses nice asymptotic properties when t→+0.

Bounded solutions of functional differential equations of the neutral type with infinite delays

1982 ◽  
Vol 93 (1-2) ◽  
pp. 33-39 ◽  
Author(s):  
V. G. Angelov ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Bounded Solutions ◽  
Initial Value ◽  
Infinite Delays ◽  
Functional Differential

SynopsisIn this paper the authors obtain sufficient conditions for the existence and uniqueness of the initial value problem of functional differential equations of neutral type with infinite delays, making use of some earlier results of the present authors.

scholarly journals D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1761
Author(s):  
Natalia Dilna ◽  
Michal Fečkan ◽  
Mykola Solovyov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Functional Differential Equations ◽  
Linear Functions ◽  
Initial Value ◽  
Nonlinear Functional ◽  
Symmetry Properties ◽  
Theoretical Investigations ◽  
Functional Differential ◽  
Symmetric Property

This paper presents a method of establishing the D-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties.

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.

On the asymptotics of solutions of a class of linear functional-differential equations

1996 ◽  
Vol 7 (5) ◽  
pp. 511-518 ◽  
Author(s):  
G. Derfel ◽  
F. Vogl
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Linear Functional ◽  
Sharp Estimate ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Asymptotics Of Solutions ◽  
Functional Differential ◽  
Image Position ◽  
Growth Of Solutions

A sharp estimate of the growth of solutions of the initial value problem for systems of the formwhere Cj(t) are matrices with elements of power growth, is found. As a corollary of this result, it follows, for instance, that each solution of the initial value problem satisfies the estimate ‖u(t)‖ ≤ Cexp{γln2(1+|t|)} for some C > 0 and γ > 0.

scholarly journals Linear Hyperbolic Functional-Differential Equations with Essentially Bounded Right-Hand Side

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Alexander Domoshnitsky ◽  
Alexander Lomtatidze ◽  
Abraham Maghakyan ◽  
Jiří Šremr
Keyword(s):  
Differential Equations ◽  
Unique Solvability ◽  
Initial Value Problem ◽  
Hyperbolic Equations ◽  
Functional Differential Equations ◽  
Linear Operators ◽  
Initial Value ◽  
Bounded Functions ◽  
Functional Differential ◽  
Characteristic Initial Value Problem

Theorems on the unique solvability and nonnegativity of solutions to the characteristic initial value problemu1,1(t,x)=l0(u)(t,x)+l1(u1,0)(t,x)+l2(u0,1)(t,x)+q(t,x),  u(t,c)=α(t)fort∈[a,b], u(a,x)=β(x)  for  x∈[c,d]given on the rectangle[a,b]×[c,d]are established, where the linear operatorsl0,l1,l2map suitable function spaces into the space of essentially bounded functions. General results are applied to the hyperbolic equations with essentially bounded coefficients and argument deviations.

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