Difference between revisions of "Differential-functional equation"
From Encyclopedia of Mathematics
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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 | + | {{TEX|done}} |
| + | 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|Differential equations, ordinary, with distributed arguments]]). | ||
====References==== | ====References==== | ||
Latest revision as of 19:04, 31 March 2017
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).
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=11808
Differential-functional equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Differential-functional_equation&oldid=11808
This article was adapted from an original article by A.D. Myshkis (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article