# Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Lemma**

**1.**

- (i)
- $H(v,G)\ge 0$ with the equality if and only if $v=0$.
- (ii)
- For every $L>0$, there exist constants ${K}_{1}={K}_{1}\left(L\right)>0,{K}_{2}={K}_{2}\left(L\right)>0$ such that$${K}_{1}{|G\left(t\right)|}^{q-2}{v}^{2}\le H(v,G)\le {K}_{2}{|G\left(t\right)|}^{q-2}{v}^{2}$$for any t and v satisfying $\left|\frac{v}{G}\right|\le L$.

**Lemma**

**2.**

**Theorem**

**1.**

## 3. Main Results

**Theorem**

**2.**

**Proof.**

**Corollary**

**1.**

**Corollary**

**2.**

**Proof.**

**Corollary**

**3.**

**Proof.**

## 4. Concluding Remarks

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Pátíková, Z.
Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation. *Mathematics* **2021**, *9*, 502.
https://doi.org/10.3390/math9050502

**AMA Style**

Pátíková Z.
Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation. *Mathematics*. 2021; 9(5):502.
https://doi.org/10.3390/math9050502

**Chicago/Turabian Style**

Pátíková, Zuzana.
2021. "Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation" *Mathematics* 9, no. 5: 502.
https://doi.org/10.3390/math9050502