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Functional differential equations

Czechoslovak Mathematical Journal, 2002
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Functional differential equations

Applicable Analysis, 1979
Using a modification of the Tawumikhin method, the authors obtain asymptotic properties of solutions os delay differential equations. In particular using Liapunov functions we obtain sufficient conditions for solutions to approach a constant c as t→∞. Here and f has appropriate smoothness properties to guarantee extendability of solutions.
Stephen R. Bernfeldt, John R. Haddock, V. Lakshmikantham   +2 more
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Mixed Functional Differential Equations

Journal of Mathematical Sciences, 2005
Definition: A functional-differential equation (FDE) for a function with more than one continuous arguments is called a mixed FDE (MFDE) if it contains a derivative of the unknown function with respect to one of the arguments only. MFDEs form a special subclass of ordinary Banach-space-valued DE with locally bounded right-hand side.
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Functional differential equations

Complex Variables, Theory and Application: An International Journal, 2001
It is shown that if an entire function f along with a finite number of its derivatives satisfies a seemingly very weak type of functional equation, then fsatisfies an algebraic differential equation. The proof involves linear algebra and Nevanlinna theory.
Fred Gross, Charles F. Osgood
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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

2018
The goal of this chapter is to apply the theories developed in the previous chapters to functional differential equations. In Section 7.1 retarded functional differential equations are rewritten as abstract Cauchy problems and the integrated semigroup theory is used to study the existence of integrated solutions and to establish a general Hopf ...
Pierre Magal, Shigui Ruan
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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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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

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

Functional Differential Equations, 1991
T. Yoshizawa, J. Kato
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