Some generalizations of delay integral inequalities of Gronwall-Bellman type with power and their applications

Haoyue Song; Fanwei Meng

doi:10.3934/mfc.2021022

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2022, Volume 5, Issue 1: 45-55. Doi: 10.3934/mfc.2021022

This issue Previous Article Sharp upper bounds on the maximum $M$-eigenvalue of fourth-order partially symmetric nonnegative tensors Next Article Bound state solutions for fractional Schrödinger-Poisson systems

Some generalizations of delay integral inequalities of Gronwall-Bellman type with power and their applications

Haoyue Song and
Fanwei Meng

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China

^* Corresponding author: Fanwei Meng
^* Corresponding author: Fanwei Meng

Received: March 2021

Revised: August 2021

Early access: October 2021

Published: February 2022

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Abstract

Noting the diverse generalizations of the Gronwall-Bellman inequality, this paper investigates some new delay integral inequalities with power, deriving explicit bound on the solution and providing an example. The inequalities given here can act as powerful tools for studying qualitative properties such as existence, uniqueness, boundedness, stability and asymptotics of solutions of differential and integral equations.

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Mathematics Subject Classification: Primary: 39A12; Secondary: 26A33.

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References

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