# The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition

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## Abstract

**:**

## 1. Introduction

## 2. Formulation of the Main Result

**Definition**

**1.**

**Theorem**

**1.**

## 3. Auxiliary Assertions

**Lemma**

**1**

**([9]**

**(p. 18)).**

**Lemma**

**2.**

## 4. Proof of Theorem 1

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Nachaoui, A.; Shavadze, T.; Tadumadze, T. The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition. *Mathematics* **2020**, *8*, 1845.
https://doi.org/10.3390/math8101845

**AMA Style**

Nachaoui A, Shavadze T, Tadumadze T. The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition. *Mathematics*. 2020; 8(10):1845.
https://doi.org/10.3390/math8101845

**Chicago/Turabian Style**

Nachaoui, A., T. Shavadze, and T. Tadumadze. 2020. "The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition" *Mathematics* 8, no. 10: 1845.
https://doi.org/10.3390/math8101845