Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Equation (1) $ (r(t)x')' + f(t)x = 0$ is regarded as a perturbation of (2) $ (r(t)y')' + g(t)y = 0$, where the latter is nonoscillatory at infinity. It is shown that if a certain improper integral involving $ f - g$ converges sufficiently rapidly (but perhaps conditionally), then (1) has a solution which behaves for large $ t$ 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.

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, Linear perturbations of a nonoscillatory second order equation, Proc. Amer. Math. Soc. 97 (1986), 423-428. MR 840623 (87g:34036)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34E10, 34C10

Retrieve articles in all journals with MSC: 34E10, 34C10

Additional Information

Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society