Annali di Matematica Pura ed Applicata

, Volume 101, Issue 1, pp 307–320 | Cite as

Continuability, boundness and asymptotic behavior of solutions ofx″ +q(t)f(x)=r(t)

  • John R. Graef
  • Paul W. Spikes


In addition to obtaining sufficient conditions for continuability of solutions of x″ + q(t)f(x)=r(t), some sufficient conditions and some necessary and sufficient conditions for boundedness are obtained. The asymptotic behavior of solutions is studied through examination of r(t)/q(t) as t → ∞.


Asymptotic Behavior 
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  1. [1]
    N. P. Bhatia,Some oscillation theorems for second order differential equations, J. Math. Anal. Appl.,15 (1966), pp. 442–446.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    T. Burton -R. Grimmer,On the asymptotic behavior of solutions of x″ + a(t)f(x)=0, Proc. Camb. Phil. Soc.,70 (1971), pp. 77–88.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M. E. Hammett,Nonoscillation properties of a nonlinear differential equation, Proc. Amer. Math. Soc.,30 (1971), pp. 92–96.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    P. W. Spikes,Behavior of the solutions of the differential equation y″ + qy p =r, Applicable Analysis, to appear.Google Scholar
  5. [5]
    P. W. Spikes,Behavior of the solutions of the differential equation y″ + qy p=r, Ph. D. Dissertation, Auburn University, 1970.Google Scholar
  6. [6]
    J. S. W. Wong,Some stability conditions for x″ + a(t)x 2n−1 =0, S.I.A.M. Jour. Appl. Math.,15 (1967), pp. 889–892.CrossRefzbMATHGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1974

Authors and Affiliations

  • John R. Graef
    • Paul W. Spikes

      There are no affiliations available

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