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.
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Agarwal, R.P., Berezansky, L., Braverman, E., Domoshnitsky, A. (2012). Linearization Methods for Nonlinear Equations with a Distributed Delay. In: Nonoscillation Theory of Functional Differential Equations with Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3455-9_10
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DOI: https://doi.org/10.1007/978-1-4614-3455-9_10
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