On the Oscillatory Behavior of Solutions of Second-Order Damped Differential Equations with Several Sub-Linear Neutral Terms
Abstract
:1. Introduction
- (A1) for are the ratios of odd positive integers;
- (A2) are continuous functions for ;
- (A3) with and as for ;
- (A4) , and there exists is a ratio of odd positive integers and a function such that , for all .
2. Preliminaries
- (i)
- , and ;
- (ii)
- is decreasing;
- (iii)
- for .
3. Main Results
4. Examples
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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El-Gaber, A.A.; El-Sheikh, M.M.A.; Rezk, H.M.; Zakarya, M.; AlNemer, G.; El-Saedy, E.I. On the Oscillatory Behavior of Solutions of Second-Order Damped Differential Equations with Several Sub-Linear Neutral Terms. Mathematics 2024, 12, 3217. https://doi.org/10.3390/math12203217
El-Gaber AA, El-Sheikh MMA, Rezk HM, Zakarya M, AlNemer G, El-Saedy EI. On the Oscillatory Behavior of Solutions of Second-Order Damped Differential Equations with Several Sub-Linear Neutral Terms. Mathematics. 2024; 12(20):3217. https://doi.org/10.3390/math12203217
Chicago/Turabian StyleEl-Gaber, A. A., M. M. A. El-Sheikh, Haytham M. Rezk, Mohammed Zakarya, Ghada AlNemer, and E. I. El-Saedy. 2024. "On the Oscillatory Behavior of Solutions of Second-Order Damped Differential Equations with Several Sub-Linear Neutral Terms" Mathematics 12, no. 20: 3217. https://doi.org/10.3390/math12203217
APA StyleEl-Gaber, A. A., El-Sheikh, M. M. A., Rezk, H. M., Zakarya, M., AlNemer, G., & El-Saedy, E. I. (2024). On the Oscillatory Behavior of Solutions of Second-Order Damped Differential Equations with Several Sub-Linear Neutral Terms. Mathematics, 12(20), 3217. https://doi.org/10.3390/math12203217