Periodic Solutions of Linear, Riccati, and Abel Dynamic Equations
We study the number of periodic solutions of linear, Riccati and Abel dynamic equations in the time scales setting. In this way, we recover known results for corresponding differential equations and obtain new results for associated difference equations. In particular, we prove that there is no upper bound for the number of isolated periodic solutions of Abel difference equations. One of the main tools introduced to get our results is a suitable Melnikov function. This is the first time that Melnikov functions are used for dynamic equations on time scales.
M. Bohner et al., "Periodic Solutions of Linear, Riccati, and Abel Dynamic Equations," Journal of Mathematical Analysis and Applications, vol. 470, no. 2, pp. 733-749, Academic Press Inc., Feb 2019.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2018.10.018
Mathematics and Statistics
Keywords and Phrases
Linear, Riccati and Abel differential and difference equations; Melnikov function; Periodic function; Time scales
International Standard Serial Number (ISSN)
Article - Journal
© 2019 Academic Press Inc., All rights reserved.