Annali di Matematica Pura ed Applicata

, Volume 82, Issue 1, pp 123–133 | Cite as

Oscillation criteria for nonlinear second order equations

  • W. J. Coles


A necessary and a sufficient condition are given for oscillation of all solutions of y″+f(t, y)=0. We sequire that a(t)α(y)≤f(t, y) if y>0, and f(t, y)<-b(t)β(y) if y<0, together with continuity and integrability assumptions on a, b, α, and β. Of speciat interest here is the relaxing of conditions a≥0, b≥0 in Machi - Wong [6].


Order Equation Oscillation Criterion Integrability Assumption Speciat Interest 
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]
    F. V. Atkinson,On second-order nonlinear oscillations, Pac. J. Math. 5 (1955), 643–647.MATHGoogle Scholar
  2. [2]
    N. P. Bhatia,Some oscillation theorems for second order differential equations, Jour. Math. Anal. Appl. 15 (1966), 442–446.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    W. B. Fite,Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math Soc. 19 (1918), 341–352.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    Jack W. Macki,Two examples in the theory of oscillations, Research Preprint, Dept. of Math. Univ. of Alberta, Ser. A, vol. 4, no 38.Google Scholar
  5. [5]
    Jack W. Macki andJ. S. W. Wong,Oscillation of solutions to second-order nonlinear differential equations, Pac. J. Math. 24 (1968), 111–117.MathSciNetGoogle Scholar
  6. [6]
    E. C. Tomastik,Oscillations of a nonlinear second order differential equation, SIAM J. 15 (1967), 1275–1277.MATHMathSciNetGoogle Scholar
  7. [7]
    P. Waltman,Oscillation of solutions of a nonlinear equation, SIAM Review 5 (1963), 128–130.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    P. Waltman,An oscillation criterion for a nonlinear second order equation, Jour. Math. Anal. Appl. 10 (1965), 439–441.CrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    A. Wintner,A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115–117.MATHMathSciNetGoogle Scholar
  10. [10]
    J. S. W. Wong,A note on second order nonlinear oscillations, SIAM Review 10 (1968), 88–91.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1969

Authors and Affiliations

  • W. J. Coles

There are no affiliations available

Personalised recommendations