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Linearization Methods for Nonlinear Equations with a Distributed Delay

In: Nonoscillation Theory of Functional Differential Equations with Applications

Author

Listed:
  • Ravi P. Agarwal

    (Texas A&M University—Kingsville, Department of Mathematics)

  • Leonid Berezansky

    (Ben-Gurion University of the Negev, Department of Mathematics)

  • Elena Braverman

    (University of Calgary, Department of Mathematics)

  • Alexander Domoshnitsky

    (Ariel University Center of Samaria, Department of Computer Sciences and Mathematics)

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.

Suggested Citation

  • Ravi P. Agarwal & Leonid Berezansky & Elena Braverman & Alexander Domoshnitsky, 2012. "Linearization Methods for Nonlinear Equations with a Distributed Delay," Springer Books, in: Nonoscillation Theory of Functional Differential Equations with Applications, edition 127, chapter 0, pages 241-262, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-3455-9_10
    DOI: 10.1007/978-1-4614-3455-9_10
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