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Functional — Differential Equations

2003
In this chapter we consider one more class of problems the solution of which can be obtained by the parametric continuation method. This is the initial value problem (the Cauchy problem) for the functional differential equations. The equations with nonlocal retarded argument and integro differential equations can be included into this class of problems.
V. I. Shalashilin, E. B. Kuznetsov
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Functional Differential Equations

1968
Lyapunov’s second method gives sufficient conditions for stability and asymptotic stability. This method has been extended in several directions.7,8 One of the interesting extension of this method depends basically on the fact that a function satisfying the inequality $$m'(t)\leq w(t,m(t)) \;\;\;\;\;\;\; m(t_{0})=r_{0}$$ is majorized by the ...
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Functional Differential Equations

2019
Equations determining a functional and involving variational derivatives are called functional differential equations (abbreviated by fde, list in Chap. 1). Definitions and elementary properties of such equations are discussed to prepare the subsequent development on fdes. Two types of such equations are considered: elliptic and parabolic fdes.
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Functional Differential Equations

1981
A distinguishing feature of ordinary differential equations is that the future behavior of solutions depends only upon the present (initial) values of the solution. Numerous physical, economic, biological, and social systems, though, exhibit hereditary dependence. That is, the future state of the system depends not only upon the present state, but also
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On Nested Functional Differential Equations

SIAM Journal on Applied Mathematics, 1970
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A unified approach to study the existence and numerical solution of functional differential equation

Applied Numerical Mathematics, 2021
Quang A Dang
exaly  

Analytic solutions of an iterative functional differential equation

Computers and Mathematics With Applications, 1997
Jian-Guo Si, Sui Sun Cheng
exaly  

Analytic Solutions of an Iterative Functional Differential Equation

Journal of Mathematical Analysis and Applications, 2001
Jian-Guo Si
exaly  

Existence of positive solutions for nonlinear fractional functional differential equation

Computers and Mathematics With Applications, 2012
Haibo Chen
exaly  

Analytic solutions of a second-order iterative functional differential equation

Computers and Mathematics With Applications, 2002
Jian-Guo Si
exaly