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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0840623-1
PII: S 0002-9939(1986)0840623-1
Article copyright: © Copyright 1986 American Mathematical Society