Abstract
This is the first part of a survey on analytic solutions of functional differential equations (FDE). Some classes of FDE that can be reduced to ordinary differential equations are considered since they often provide an insight into the structure of analytic solutions to equations with more general argument deviations. Reducible FDE also find important applications in the study of stability of differential‐difference equations and arise in a number of biological models.
Highlights
In [1,2,3,4] a method has been discovered for the study of a special class of functional differential equations differential equations with involutions
Suppose we are given a differential equation with reflection of order n with constant coefficients n 7
A necessary and sufficient condition for the reducibility of a functional differential equations (FDE) to a system of ordinary differential equations is given by the author of [30]
Summary
In [1,2,3,4] a method has been discovered for the study of a special class of functional differential equations differential equations with involutions. (i) The function f(t) is a continuously differentiable strong involution with a fixed point tO. Where x is an unknown function and where the following conditions are fulfilled: fl’ (I) The functions f n form a finite group of order n with respect to fl(t) superposition of functions, t, and map the open set G into G, G being the largest open set wherein all expressions appearing in this paper are defined. If conditions (1)-(3) are satisfied, every p-times differentiable solution of Eq (2.14) is a component of the solution of a system of ordinary differential equations with argument t only In order that the solution of this equation satisfies problem (3.1)-(3.2), we need to pose the following initial conditions for (3.4): the values of the function x(t) and of its n 1 derivatives at the point t O should equal Xk, k O, n i, from (3.2), while the values (n).
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