## Pacific Journal of Mathematics

### On the asymptotic behavior of solutions of $x''+a(t)f(x)=e(t)$.

#### Article information

Source
Pacific J. Math., Volume 41, Number 1 (1972), 43-55.

Dates
First available in Project Euclid: 13 December 2004

https://projecteuclid.org/euclid.pjm/1102968416

Mathematical Reviews number (MathSciNet)
MR0310359

Zentralblatt MATH identifier
0245.34024

Subjects
Primary: 34D05: Asymptotic properties

#### Citation

Burton, T.; Grimmer, R. On the asymptotic behavior of solutions of $x''+a(t)f(x)=e(t)$. Pacific J. Math. 41 (1972), no. 1, 43--55. https://projecteuclid.org/euclid.pjm/1102968416

#### References

• [1] R. Bellman, Stability Theory of DifferentialEquations, Dover, New York, 1969.
• [2] T. A. Burton and R. C. Grimmer, Stabilityproperties of (r(t)u'Y + a(t)f(u)g(u') =
• [3] T. A. Burton and R. C. Grimmer, On the asymptotic behavior of solutions of x" + a(t)f(x) = 0, Proc. Cam- bridge Philos. Soc, 70 (1971), 77-88.
• [4] T. A. Burton and R. C. Grimmer, On continuability of second order differential equations, Proc. Amer. Math. Soc, 29 (1971), 277-283.
• [5] L. Cesari, Asymptotic Behavior and StabilityProblems in OrdinaryDifferential Equations, Academic Press, New York, 1963.
• [6] C. V. Coffman and D. F. Ulrich, On the continuation of solutions of a certain non- linear differentialequation, Monatsh. Math., 71 (1967), 385-392.
• [7] E. Hille, Lectures on Ordinary DifferentialEquations,Addison Wesley, Reading, Massachusetts, 1969.
• [8] D. B. Hinton, Some stability conditions for yn 4- qy = 0, J. Math. Anal. Appl., 21 (1968), 126-131.
• [9] D. B. Hinton, Some stability conditions for a nonlineardifferentialequation, Trans. Amer. Math. Soc, 139 (1969), 349-358.
• [10] V. Lakshmikantham and S. Leela, Differentialand IntegralInequalitiesvol. 1, Academic Press, New York, 1969.
• [11] A. C. Lazer, Stability condition for the differentialequation yrf + p{x)y = 0, Michigan Math. J., 12 (1965), 193-196.
• [12] D. Wilett and J. S. W. Wong, Some properties of [p(t)x'Y Jrq(t)f(x) =O,J. Math. Anal., Appl., 23 (1968), 15-24.
• [13] J. S. W. Wong, Some stabilityconditions for xtf + ().2%~1 = 0, SIAM J. Appl. Math., 15 (1967), 889-892.
• [14] J. S. W. Wong,Remarks on stability conditions for the differentialequation x" + a(t) f(x) = 0, J. Austral. Math. Soc, IX (1969), 496-502.
• [15] T. Yoshizawa, Stability Theory by Liapunov''s Second Method, Math. Soc. Japan, Tokyo, 1967.