# Linearization Methods for Nonlinear Equations with a Distributed Delay

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## Abstract

Chapter 10 deals with the linearized oscillation and nonoscillation theory for a rather general nonlinear differential equation with a distributed delay. As corollaries, oscillation and nonoscillation linearized theorems are obtained for most known classes of nonlinear functional differential equations: delay differential equations, integrodifferential equations and mixed differential equations. Explicit oscillation and nonoscillation results are obtained for the logistic delay differential equation with a distributed delay, the Lasota-Wazewska equation, and Nicholson’s blowflies equation, as applications of the general results.

Another approach to oscillation problems for nonlinear differential equations with a distributed delay is described by so called Mean Value Theorem when their study is reduced to the investigation of either a nonlinear or a linear equation with a single concentrated delay. This theorem allows to reduce an oscillation/nonoscillation problem for a nonlinear equation with a distributed delay to the same problem for a specially constructed linear delay differential equation.

## Keywords

Delay Distribution Contralateral Delay Non-oscillatory Results Blowﬂies Equation General Nonlinear Differential Equation## References

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