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Equivalence Transformation for Neutral Differential Equations: Oscillation of Solutions

Ağacık Zafer, Tuncay Candan () and Zeynep Nilhan Gürkan
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Ağacık Zafer: College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait
Tuncay Candan: College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait
Zeynep Nilhan Gürkan: College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait

Mathematics, 2025, vol. 13, issue 14, 1-11

Abstract: We introduce an equivalence transformation to study the oscillation behavior of solutions for linear neutral differential equations of canonical and noncanonical types. The new approach leads to several novel oscillation criteria. Moreover, we show that the same arguments can be applied to nonlinear neutral equations under suitable monotonicity conditions. The importance of the results is also supported by examples.

Keywords: second-order; neutral equation; canonical; noncanonical; oscillation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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