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September 10, 2025Open Access

Second order neutral delay differential equations and their oscillatory criteria derived by linearization

Key Points

New oscillatory criteria for second-order neutral delay differential equations were established, enhancing existing methods.
The study emphasizes monotonicity properties of non-oscillatory solutions to understand oscillatory behavior.
Linearization plays a crucial role in deriving new criteria, refining the approach to analyze these equations.
The findings support the need for improved criteria in the analysis of oscillatory behaviors in mathematical equations.

Abstract

In this paper, we investigate the oscillatory behavior of second-order neutral delay differential equations with a canonical operator of the form ( a ( x ) ( v ′ ( x ) ) m ) ′ + C ( x , u ( φ ( x ) ) ) = 0. We introduce new monotonicity properties of the non-oscillatory solutions of these equations, which are then used to linearize the equations and derive new oscillatory criteria. The presented results significantly improve upon existing criteria.

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Discussion

Journals

Electronic journal of qualitative theory of differential equations

Institutions

Erciyes University

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