New Oscillation Theorems for Second-Order Superlinear Neutral Differential Equations with Variable Damping Terms

Aldiaiji, Munirah; Qaraad, Belgees; Iambor, Loredana Florentina; Elabbasy, Elmetwally M.

doi:10.3390/sym15091630

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…On the other hand, we do not need more additional conditions, such as (8). By utilising the results provided in the reference [34], we establish new oscillation criteria for Equation (1). Based on the above, we aim in this paper to complete, simplify, and develop previous results.…”

Section: Motivationmentioning

confidence: 99%

Second-Order Damped Differential Equations with Superlinear Neutral Term: New Criteria for Oscillation

Al-Jaser,

Cesarano,

Qaraad

et al. 2024

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This paper focuses on establishing new criteria to guarantee the oscillation of solutions for second-order differential equations with a superlinear and a damping term. New sufficient conditions are presented, aimed at analysing the oscillatory properties of the solutions to the equation under study. To prove these results, we employed various analysis methods, establishing new relationships to address certain problems that have hindered previous research. Consequently, by applying the principles of comparison and the Riccati transformation, we obtained findings that develop and complement those reported in earlier literature. The significance of our results is illustrated with several examples.

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Section: Motivationmentioning

confidence: 99%

Second-Order Damped Differential Equations with Superlinear Neutral Term: New Criteria for Oscillation

Al-Jaser,

Cesarano,

Qaraad

et al. 2024

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New Conditions for Testing the Oscillation of Solutions of Second-Order Nonlinear Differential Equations with Damped Term

Al-Jaser,

Qaraad,

Ramos

et al. 2024

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This paper deals with the oscillatory behavior of solutions of a new class of second-order nonlinear differential equations. In contrast to most of the previous results in the literature, we establish some new criteria that guarantee the oscillation of all solutions of the studied equation without additional restrictions. Our approach improves the standard integral averaging technique to obtain simpler oscillation theorems for new classes of nonlinear differential equations. Two examples are presented to illustrate the importance of our findings.

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Oscillation of Third-Order Differential Equations with Advanced Arguments

Aldiaiji,

Qaraad,

Iambor

et al. 2023

Mathematics

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The main objective of this work was to study some oscillatory and asymptotic properties of a new class of advanced neutral differential equations. Using new relations to link the solution and its corresponding function, we introduced new oscillatory criteria that aim to enhance, simplify, and complement some of current results. We provide some examples to demonstrate the significance of our results.

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New Oscillation Theorems for Second-Order Superlinear Neutral Differential Equations with Variable Damping Terms

Cited by 3 publications

References 25 publications

Second-Order Damped Differential Equations with Superlinear Neutral Term: New Criteria for Oscillation

Second-Order Damped Differential Equations with Superlinear Neutral Term: New Criteria for Oscillation

New Conditions for Testing the Oscillation of Solutions of Second-Order Nonlinear Differential Equations with Damped Term

Oscillation of Third-Order Differential Equations with Advanced Arguments

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