## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2019 (2019), Article ID 2523615, 9 pages.

### Results on Uniqueness of Solution of Nonhomogeneous Impulsive Retarded Equation Using the Generalized Ordinary Differential Equation

D. K. Igobi and U. Abasiekwere

#### Abstract

In this work, we consider an initial value problem of a nonhomogeneous retarded functional equation coupled with the impulsive term. The fundamental matrix theorem is employed to derive the integral equivalent of the equation which is Lebesgue integrable. The integral equivalent equation with impulses satisfying the Carathéodory and Lipschitz conditions is embedded in the space of generalized ordinary differential equations (GODEs), and the correspondence between the generalized ordinary differential equation and the nonhomogeneous retarded equation coupled with impulsive term is established by the construction of a local flow by means of a topological dynamic satisfying certain technical conditions. The uniqueness of the equation solution is proved. The results obtained follow the primitive Riemann concept of integration from a simple understanding.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2019 (2019), Article ID 2523615, 9 pages.

**Dates**

Received: 5 January 2019

Accepted: 5 March 2019

First available in Project Euclid: 16 May 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1557972301

**Digital Object Identifier**

doi:10.1155/2019/2523615

#### Citation

Igobi, D. K.; Abasiekwere, U. Results on Uniqueness of Solution of Nonhomogeneous Impulsive Retarded Equation Using the Generalized Ordinary Differential Equation. Int. J. Differ. Equ. 2019 (2019), Article ID 2523615, 9 pages. doi:10.1155/2019/2523615. https://projecteuclid.org/euclid.ijde/1557972301