scholarly journals Comparison theorems for functional differential equations with deviating arguments

1981 ◽  
Vol 33 (3) ◽  
pp. 509-532 ◽  
Author(s):  
Taka\^{s}i KUSANO ◽  
Manabu NAITO
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Comparison Theorems ◽  
Deviating Arguments ◽  
Functional Differential

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

scholarly journals Oscillation Properties for Systems of Higher-Order Partial Differential Equations with Distributed Deviating Arguments

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Youjun Liu ◽  
Jianwen Zhang ◽  
Jurang Yan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Partial Differential ◽  
Deviating Arguments ◽  
Distributed Deviating Arguments ◽  
Functional Differential ◽  
Oscillation Properties

New sufficient conditions are obtained for oscillation for the solutions of systems of a class of higher-order quasilinear partial functional differential equations with distributed deviating arguments. The obtained results are illustrated by example.

INVESTIGATION OF THE IMPACT OF DELAY IN ONE MATHEMATICAL MODEL OF WORLD DEVELOPMENT DYNAMICS

2021 ◽  
Vol 6 ◽  
pp. 47-54
Author(s):  
Denis Khusainov ◽  
◽  
Andrey Shatyrko ◽  
Alexey Bychkov ◽  
Bedrick Puza ◽  
...  
Keyword(s):  
Differential Equations ◽  
Time Lag ◽  
Functional Differential Equations ◽  
Deviating Arguments ◽  
System Equilibrium ◽  
Constant Coefficients ◽  
Functional Differential ◽  
The Stability ◽  
The Impact ◽  
World Development

There is a large number of works devoted to the dynamics of world development. But very few of them have clear abstract mathematical models of the corresponding processes. This work is devoted to further deepening and mathematical abstraction of the study of world development process. The qualitative analysis of linear and modified nonlinear model in the form of systems of inhomogeneous differential equations is carried out. Their steady states are calculated, explicit analytical solutions are presented. For the first time, a model taking into account the time delay factor is proposed, which is written in the form of functional-differential equations with argument deviation. It is shown that with such an introduction to the model of a delayed argument, the system can be reduced to a system of linear inhomogeneous differential equations with constant coefficients without delay, and the stability of the steady state of the system equilibrium under study will be affected only by linear terms of equations without argument deviation. This fact well correlates with the socio-economic interpretation of this problem. In the future, the work will focus on studying the influence of not one but several factors of time lag, when the model is presented as a system of functional-differential equations with several different deviating arguments in equations responsible for the dynamics of a particular process dynamics of world development.

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