Differential-functional equation

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An equation relating the argument and the unknown function and its derivatives, generally taken with a functionally transformed argument. Here, the expression of the functional transformation may include the unknown function, as a result of which the equation may contain combinations such as $y'(y(x))$, etc. The concept of a differential-functional equation is often understood to be the synonym of an ordinary differential equation with deviating or distributed arguments (cf. Differential equations, ordinary, with distributed arguments).


[1] E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 1. Gewöhnliche Differentialgleichungen , Chelsea, reprint (1947)


Instead of differential-functional equation one often uses the phrase functional-differential equation.


[a1] J.K. Hale, "Functional differential equations" , Springer (1971)
How to Cite This Entry:
Differential-functional equation. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.D. Myshkis (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article