ASYMPTOTIC AND OSCILLATORY BEHAVIOR OF DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS AND A NONLINEAR NEGATIVE NEUTRAL TERM

M. Botros; Wedad Albalawi; Mohammad Jazmati; Osama Moaaz

doi:10.11948/20250210

2027 Volume 17 Issue 2

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M. Botros, Wedad Albalawi, Mohammad Jazmati, Osama Moaaz. ASYMPTOTIC AND OSCILLATORY BEHAVIOR OF DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS AND A NONLINEAR NEGATIVE NEUTRAL TERM[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 948-962. doi: 10.11948/20250210

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M. Botros, Wedad Albalawi, Mohammad Jazmati, Osama Moaaz. ASYMPTOTIC AND OSCILLATORY BEHAVIOR OF DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS AND A NONLINEAR NEGATIVE NEUTRAL TERM[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 948-962. doi: 10.11948/20250210

ASYMPTOTIC AND OSCILLATORY BEHAVIOR OF DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS AND A NONLINEAR NEGATIVE NEUTRAL TERM

1.
Basic Science Department, Faculty of Engineering, Delta University for Science and Technology, P.O. Box 11152, Gamasa, Egypt
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Author Bio: Email: monica.botros@deltauniv.edu.eg(M. Botros); Email: wsalbalawi@pnu.edu.sa(W. Albalawi); Email: Jzmaty@qu.edu.sa(M. Jazmati)
Corresponding author: Email: o.refaei@qu.edu.sa(O. Moaaz)

Abstract

Abstract

This study covers the oscillatory characteristics of solutions of delay differential equations. In order to test the oscillation of all solutions, we establish three distinct criteria and take into account the noncanonical situation. The purpose of establishing various criteria is to achieve a number of benefits in the oscillation test, namely applying the criterion to Euler's equation yields the sharp condition, the influence of delay function of the criterion, and applying to some cases that have not been studied previously. In previous works that treated the studied equation in its general form, only classical criteria were obtained for the canonical case. Finally, we demonstrate that our findings are a generalization and extension of earlier findings in the literature through discussion and examples.
- Differential equation /
- asymptotic and oscillatory behavior /
- nonlinear negative neutral term /
- Riccati technique
MSC: 34C1082, 34K11

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References

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