© 2018 Elsevier Inc. 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.
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 15 Feb 2019|
- Linear, Riccati and Abel differential and difference equations
- Melnikov function
- Periodic function
- Time scales