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Odd-order differential equations with deviating arguments: asymptomatic behavior and oscillation.

A Muhib1,2, I Dassios3, D Baleanu4,5,6

  • 1Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.

Mathematical Biosciences and Engineering : MBE
|February 9, 2022
PubMed
Summary
This summary is machine-generated.

This study investigates the oscillatory behavior of odd-order delay differential equations with deviating arguments. New criteria were developed to analyze oscillation, extending existing research in the field.

Keywords:
asymptotic behaviordifferential equation with deviating argumentneutralodd-orderoscillation

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Area of Science:

  • Mathematics
  • Differential Equations
  • Oscillation Theory

Background:

  • Delay differential equations (DDEs) are crucial in modeling systems with time delays.
  • Research on the oscillatory behavior of even-order DDEs is extensive.
  • Odd-order DDEs with deviating arguments remain less explored, highlighting a gap in current literature.

Purpose of the Study:

  • To analyze the oscillatory behavior of two specific classes of odd-order delay differential equations.
  • To develop novel criteria for determining oscillation in these equations.
  • To extend and complement existing findings on DDE oscillation.

Main Methods:

  • Development of analytical techniques tailored for odd-order DDEs.
  • Application of multiple methods to derive oscillation criteria.
  • Comparison and integration of results with established literature.

Main Results:

  • Established multiple new criteria for assessing the oscillatory nature of the studied DDEs.
  • Demonstrated the effectiveness of the developed methods in analyzing oscillation.
  • Provided a theoretical foundation for further research into odd-order DDEs.

Conclusions:

  • The study successfully addresses the under-researched area of odd-order DDE oscillation.
  • The derived criteria offer valuable tools for analyzing complex oscillatory behaviors.
  • Findings significantly contribute to the broader field of delay differential equations research.