On perturbation of unstable second order linear differential equations
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- by L. Hatvani and L. Pintér PDF
- Proc. Amer. Math. Soc. 61 (1976), 36-38 Request permission
Abstract:
In connection with a conjecture of J. M. Bownds, conditions will be given on the fundamental system of the solutions of the unstable differential equation $y'' + a(t)y = 0$ which assure that the differential equation $x'' + a(t)x = g(t,x,x’)$ has a solution with the property \[ \lim \sup (|x(t)| + |x’(t)|) = \infty \quad {\text {as }}t \to \infty ,\] provided that $g(t,x,x’)$ is “sufficiently small".References
- John M. Bownds, Stability implications on the asymptotic behavior of second order differential equations, Proc. Amer. Math. Soc. 39 (1973), 169–172. MR 313596, DOI 10.1090/S0002-9939-1973-0313596-9
- W. A. Coppel, Stability and asymptotic behavior of differential equations, D. C. Heath and Company, Boston, Mass., 1965. MR 0190463
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 36-38
- MSC: Primary 34D10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0422784-5
- MathSciNet review: 0422784