Neutral Delay Differential Equations: Oscillation Conditions for the Solutions

Bazighifan, Omar; Alotaibi, Hammad; Mousa, Abd Allah A.

doi:10.3390/sym13010101

Cited by 32 publications

(21 citation statements)

References 22 publications

(31 reference statements)

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“…Exploring the past few years, the asymptotic behavior of non-linear neutral differential equations has become a significant research area in different disciplines. In context of oscillation theory, it has been the object of research for many academics, who have investigated this notion for non-linear neutral differential and difference equations; the reader can refer to [2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

2021

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The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

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Section: Introductionmentioning

confidence: 99%

Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

2021

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“…Delay differential equations contribute to many applications such as torsional oscillations which have been observed during earthquakes, see [1]. However, oscillation theory has gained particular attention due to its widespread applications in mechanical oscillations, earthquake structures, clinical applications, frequency measurements and harmonic oscillator which involves symmetrical properties; see [2,3]. In context of oscillation theory, it has been the object of many researchers who have investigated this notion for non-linear neutral differential and difference equations; the reader can refer to [4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

More Effective Conditions for Oscillatory Properties of Differential Equations

et al. 2021

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In this work, we present several oscillation criteria for higher-order nonlinear delay differential equation with middle term. Our approach is based on the use of Riccati substitution, the integral averaging technique and the comparison technique. The symmetry contributes to deciding the right way to study oscillation of solutions of this equations. Our results unify and improve some known results for differential equations with middle term. Some illustrative examples are provided.

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“…In recent years, and in context of oscillation theory, many studies have been devoted to the oscillation conditions for non-linear delay differential equations; the reader can refer to [8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%