# Approximation of a Linear Autonomous Differential Equation with Small Delay

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## Abstract

**:**

## 1. Introduction

## 2. Main Results

#### 2.1. Solution of the Matrix Equation and Its Approximation

**Theorem**

**1.**

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Proof.**

**Lemma**

**3.**

**Proof.**

**Proof of**

**Theorem 1.**

**Theorem**

**2.**

**Proof.**

#### 2.2. Dominant Eigenvalues and Eigensolutions

**Theorem**

**3.**

**Lemma**

**4.**

**Proof.**

**Lemma**

**5.**

**Proof.**

**Lemma**

**6.**

**Proof.**

**Proof of**

**Theorem 3.**

#### 2.3. Asymptotic Equivalence

**Proposition**

**1.**

**Theorem**

**4.**

**Proof.**

#### 2.4. Approximation of the Dominant Eigenvalues

**Proposition**

**2.**

**Theorem**

**5.**

## 3. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Fehér, Á.; Márton, L.; Pituk, M.
Approximation of a Linear Autonomous Differential Equation with Small Delay. *Symmetry* **2019**, *11*, 1299.
https://doi.org/10.3390/sym11101299

**AMA Style**

Fehér Á, Márton L, Pituk M.
Approximation of a Linear Autonomous Differential Equation with Small Delay. *Symmetry*. 2019; 11(10):1299.
https://doi.org/10.3390/sym11101299

**Chicago/Turabian Style**

Fehér, Áron, Lorinc Márton, and Mihály Pituk.
2019. "Approximation of a Linear Autonomous Differential Equation with Small Delay" *Symmetry* 11, no. 10: 1299.
https://doi.org/10.3390/sym11101299