Oscillation Theory

  • Saber N. Elaydi
Part of the Undergraduate Texts in Mathematics book series (UTM)


In previous chapters we were mainly interested in the asymptotic behavior of solutions of difference equations both scalar and nonscalar. In this chapter we will go beyond the question of stability and asymptoticity. Of particular interest is to know whether a solution x(n) oscillates around an equilibrium point x*, regardless of its asymptotic behavior. Since we may assume without loss of generality that x* = 0, the question that we will address here is whether solutions oscillate around zero or whether solutions are eventually positive or eventually negative.


Equilibrium Point Difference Equation Oscillatory Behavior Order Equation Delay Differential Equation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    L.H. Erbe and B.G. Zhang, Oscillation of Discrete Analogues of Delay Equations, Differential and Integral Equations, vol. 2, 1989, pp. 300–309.MathSciNetzbMATHGoogle Scholar
  2. [2]
    I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Claredon, Oxford 1991.Google Scholar
  3. [3]
    J.W. Hooker and W.T. Patula, “Riccati Type Transformation for Second Order Linear Difference Equations,” J. Math. Anal. Appl. 82 (1981), 451–462.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    R.P. Agarwal, Difference Equations and Inequalities, Theory, Methods and Applications, Marcel Dekker, New York, 1992.zbMATHGoogle Scholar
  5. [5]
    R Harman, “Difference Equations: Disconjugacy, Principal Solutions, Green’s Functions, Complete Monotonicity,” Trans. Amer. Math. Soc. 246 (1978), 1–30.MathSciNetGoogle Scholar
  6. [6]
    W.G. Kelley and A.C. Peterson, Difference Equations, An Introduction with Applications, Academic, New York 1991.zbMATHGoogle Scholar
  7. [7]
    W.T. Patula, “Growth and Oscillation Properties of Second Order Linear Difference Equations,” Siam J. Math. Anal. 19 (1979), 55–61.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Saber N. Elaydi
    • 1
  1. 1.Department of MathematicsTrinity UniversitySan AntonioUSA

Personalised recommendations