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Second-Order Delay Differential Equations

  • Ravi P. Agarwal
  • Leonid Berezansky
  • Elena Braverman
  • Alexander Domoshnitsky
Chapter
  • 937 Downloads

Abstract

Equations of the second order are popular due to their numerous applications. For equations of the second order with several delays and not including explicitly the first derivative, Chap. 7 presents nonoscillation criteria in the terms of the fundamental function of the equation and the generalized Riccati inequality. In addition, the chapter includes comparison results, explicit nonoscillation and oscillation conditions, the result that the equation is oscillatory if and only if it has a slowly oscillating solution, and explicit nonoscillation conditions which are obtained by substituting specific solutions of the generalized Riccati inequality. Sufficient conditions for positivity of a solution of the initial value problem are also presented in Chap. 7.

Keywords

Second-order Delay Differential Equations Nonoscillation Criteria Nonoscillation Conditions Non-oscillatory Property Discontinuous Parameters 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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