Novel iterative criteria for oscillatory behavior in nonlinear neutral differential equations

Fahd Masood; Salma Aljawi; Omar Bazighifan; Fahd Masood; Salma Aljawi; Omar Bazighifan

doi:10.3934/math.2025319

AIMS Mathematics

2025, Volume 10, Issue 3: 6981-7000. doi: 10.3934/math.2025319

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Research article

Novel iterative criteria for oscillatory behavior in nonlinear neutral differential equations

1.
Jadara Research Center, Jadara University, Irbid 21110, Jordan
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, 00186 Rome, Italy

Received: 22 January 2025 Revised: 01 March 2025 Accepted: 11 March 2025 Published: 26 March 2025
MSC : 34C10, 34K11

The purpose of this study was to investigate the oscillation criteria for nonlinear second-order neutral differential equations with deviating arguments, with a particular emphasis on their non-canonical forms. The primary goal was to expand the current theoretical framework by introducing new relations that improved the monotonicity of positive solutions. To attain this purpose, an iterative technique was used to deduce new oscillation criteria, which helped to enhance present understanding in this field. The study process was based on a thorough review of previous literature, followed by the creation of new oscillation criteria with both theoretical and applied significance. The obtained results were validated by three illustrative instances, demonstrating the importance and influence of these criteria in the study of neutral differential equations, particularly in the study of neutral differential equations, especially in nonlinear contexts.
- oscillatory behavior,
- differential equations,
- deviating arguments,
- noncanonical form,
- nonlinear equations, second order
Citation: Fahd Masood, Salma Aljawi, Omar Bazighifan. Novel iterative criteria for oscillatory behavior in nonlinear neutral differential equations[J]. AIMS Mathematics, 2025, 10(3): 6981-7000. doi: 10.3934/math.2025319

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Abstract

The purpose of this study was to investigate the oscillation criteria for nonlinear second-order neutral differential equations with deviating arguments, with a particular emphasis on their non-canonical forms. The primary goal was to expand the current theoretical framework by introducing new relations that improved the monotonicity of positive solutions. To attain this purpose, an iterative technique was used to deduce new oscillation criteria, which helped to enhance present understanding in this field. The study process was based on a thorough review of previous literature, followed by the creation of new oscillation criteria with both theoretical and applied significance. The obtained results were validated by three illustrative instances, demonstrating the importance and influence of these criteria in the study of neutral differential equations, particularly in the study of neutral differential equations, especially in nonlinear contexts.

References

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