Asymptotic integration of a second order ordinary differential equation
Author: Jaromír Šimša
Journal: Proc. Amer. Math. Soc. 101 (1987), 96-100
MSC: Primary 34E10; Secondary 34C10
MathSciNet review: 897077
Abstract: Equation (1) is regarded as a perturbation of (2) , where the latter is nonoscillatory at infinity. It is shown that if a certain improper integral involving converges sufficiently rapidly (but perhaps conditionally), then (1) has a solution which behaves for large like a principal solution of (2). The proof of this result is presented in such a way that it also yields as a by-product an improvement on a recent related result of Trench.
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