Abstract
This work is devoted to the prove of the existence of solutions for a semilinear retarded differential equation with infinite delay and impulses on timescales, which is done by using a version of the Arzela-Ascoli theorem on time-scales, and applying the Leray-Schauder alternative. After that, the uniqueness of solutions is proved by applying a version of Gronwall's inequality for impulsive differential equations, and finally, the continuation of solutions is proved.
| Original language | English |
|---|---|
| Pages (from-to) | 155-168 |
| Number of pages | 14 |
| Journal | Nonlinear Dynamics and Systems Theory |
| Volume | 22 |
| Issue number | 2 |
| Publication status | Published - 2022 |
Keywords
- Leray-Schauder alternative
- continuation
- existence
- infinite delay
- infinite impulses
- semilinear functional dynamic equations
- time-scales
- uniqueness
ASJC Scopus subject areas
- Mathematical Physics
- Applied Mathematics