Linearization Methods for Nonlinear Equations with a Distributed Delay

  • Ravi P. Agarwal
  • Leonid Berezansky
  • Elena Braverman
  • Alexander Domoshnitsky


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.


Delay Distribution Contralateral Delay Non-oscillatory Results Blowflies Equation General Nonlinear Differential Equation 
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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Ravi P. Agarwal
    • 1
  • Leonid Berezansky
    • 2
  • Elena Braverman
    • 3
  • Alexander Domoshnitsky
    • 4
  1. 1.Department of MathematicsTexas A&M University—KingsvilleKingsvilleUSA
  2. 2.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael
  3. 3.Department of MathematicsUniversity of CalgaryCalgaryCanada
  4. 4.Department of Computer Sciences and MathematicsAriel University Center of SamariaArielIsrael

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