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Linear perturbations of a nonoscillatory second order equation

Author: William F. Trench
Journal: Proc. Amer. Math. Soc. 97 (1986), 423-428
MSC: Primary 34C10
MathSciNet review: 840623
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Abstract: It is shown that the equation $ (r(t)x')' + g(t)x = 0$ has solutions which behave asymptotically like those of a nonoscillatory equation $ (r(t)y')' + f(t)y = 0$, provided that a certain integral involving $ f - g$ converges (perhaps conditionally) and satisfies a second condition which has to do with its order of convergence. The result improves upon a theorem of Hartman and Wintner.

References [Enhancements On Off] (What's this?)

  • [1] P. Hartman, Ordinary differential equations, Wiley, New York, 1964. MR 0171038 (30:1270)
  • [2] W. F. Trench, Functional perturbations of second order differential equations, SIAM J. Math. Anal. 16 (1985), 741-756. MR 793919 (87e:34138)

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Article copyright: © Copyright 1986 American Mathematical Society

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