Differential-functional equation
From Encyclopedia of Mathematics
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 , 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).
References
[1] | E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 1. Gewöhnliche Differentialgleichungen , Chelsea, reprint (1947) |
Comments
Instead of differential-functional equation one often uses the phrase functional-differential equation.
References
[a1] | J.K. Hale, "Functional differential equations" , Springer (1971) |
How to Cite This Entry:
Differential-functional equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Differential-functional_equation&oldid=40760
Differential-functional equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Differential-functional_equation&oldid=40760
This article was adapted from an original article by A.D. Myshkis (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article