Oscillation of Second Order Nonlinear Differential Equations with a Damping Term

Mi, Xue

doi:10.11648/j.acm.20160502.12

ACM

2016

DOI: 10.11648/j.acm.20160502.12

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Oscillation of Second Order Nonlinear Differential Equations with a Damping Term

Xue Mi¹

Abstract: A class of second-order nonlinear differential equations with a damping term is investigated in this paper. By using the Riccati transformation technique and general weight functions, we obtain some new sufficient conditions for the oscillation of the equation. Our results improve and extend some known results. Two examples are given to illustrate the main results.

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2024

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A class of time-varying differential equations for vibration research and application

Zhao,

Zhou,

et al. 2024

MATH

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<p>As a pivotal branch within the realm of differential equations, the theory of oscillation holds a crucial position in the exploration of natural sciences and the construction of modern control theory frameworks. Despite the extensive research conducted globally, focusing on individual or combined analyses of key elements such as explicit damping terms, positive and negative coefficients, time-varying delays, and nonlinear neutral terms, systematic investigations into the oscillatory behavior of even-order differential equations that concurrently embody these four complex characteristics remain scarce. This paper, by establishing reasonable assumptions, innovatively presents two crucial criteria, aiming to preliminary delve into the oscillation patterns of even-order differential equations under specific complex settings. In the course of the study, a variety of mathematical techniques, such as Riccati transformation, calculus scaling methods, and partial integration, have been utilized by the researchers to perform the necessary derivations and confirmations.</p>

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A class of time-varying differential equations for vibration research and application

Zhao,

Zhou,

et al. 2024

MATH

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show abstract

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Oscillation of Second Order Nonlinear Differential Equations with a Damping Term

Cited by 1 publication

References 30 publications

A class of time-varying differential equations for vibration research and application

A class of time-varying differential equations for vibration research and application

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