Existence and Uniqueness of Solutions for a Semilinear Functional Dynamic Equation with Infinite Delay and Impulses

C. Duque, H. Leiva, A. Tridane

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)155-168
Number of pages14
JournalNonlinear Dynamics and Systems Theory
Volume22
Issue number2
Publication statusPublished - 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

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