Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T05:02:00.648Z Has data issue: false hasContentIssue false
  • English
  • Français

A transformation to linearity of some non-linear differential-difference equations

Published online by Cambridge University Press:  17 February 2009

A. J. Bracken
A. J. Bracken
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Queensland 4067
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The problem of solving a differential-difference equation with quadratic non-linearities of a certain type is reduced to the problem of solving an associated linear differential-difference equation.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 4 , April 1982 , pp. 416 - 419
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Bellman, R. and Cooke, K. L., Differential-difference equations (Academic Press, New York, 1963).Google Scholar
[2]de Bruijn, N. G., “The difference-differential equation F′(x) = e αx+βF(x − 1). I, II”, Nederl. Akad. Wetensch. Proc. Ser. A 56 (also published as: Indagariones Math. 15) (1953), 449–458, 459–464.CrossRefGoogle Scholar
[3]Kato, T. and McLeod, J. B., “The functional-differential equation y′(x) = ay(λx) + by(x)”, Bull. Amer. Math. Soc. 77 (1971), 891–937.Google Scholar
[4]Mahler, K., “On a special functional equation”, J. London Math. Soc. 15 (1940), 115–123.CrossRefGoogle Scholar