Formulas of Bendixson and Alekseev for Difference Equations
Abstract
A well-known formula of Bendixson states that solutions of first-order differential equations, as functions of their initial conditions, satisfy a certain partial differential equation. A consequence is Alekseev's nonlinear variation of parameters formula. In this paper, corresponding results are proved for difference equations. To achieve this, use is made of the recently introduced concept of alpha derivatives, rather than of differences or of the usual derivatives. This technique allows the results to be generalized to alpha dynamic equations, which include among others ordinary differential and difference equations.
Recommended Citation
V. Lakshmikantham and M. Bohner, "Formulas of Bendixson and Alekseev for Difference Equations," Bulletin of London Mathematical Society, London Mathematical Society, Jan 2004.
The definitive version is available at https://doi.org/10.1112/S0024609303002753
Department(s)
Mathematics and Statistics
Keywords and Phrases
Alekseev; Bendixson; alpha derivatives; difference equations
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2004 London Mathematical Society, All rights reserved.
Publication Date
01 Jan 2004
