Axioms (Oct 2024)

Second-Order Neutral Differential Equations with a Sublinear Neutral Term: Examining the Oscillatory Behavior

  • Ahmed Alemam,
  • Asma Al-Jaser,
  • Osama Moaaz,
  • Fahd Masood,
  • Hamdy El-Metwally

DOI
https://doi.org/10.3390/axioms13100681
Journal volume & issue
Vol. 13, no. 10
p. 681

Abstract

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This article highlights the oscillatory properties of second-order Emden–Fowler delay differential equations featuring sublinear neutral terms and multiple delays, encompassing both canonical and noncanonical cases. Through the proofs of several theorems, we investigate criteria for the oscillation of all solutions to the equations under study. By employing the Riccati technique in various ways, we derive results that expand the scope of previous research and enhance the cognitive understanding of this mathematical domain. Additionally, we provide three illustrative examples to demonstrate the validity and applicability of our findings.

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