Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Exponential estimates for solutions of $ y\sp{''}-q\sp{2}y=0$

Author: T. T. Read
Journal: Proc. Amer. Math. Soc. 45 (1974), 332-338
MSC: Primary 34D05
MathSciNet review: 0344611
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown for any nonnegative continuous function $ q$ on $ [0,\infty )$ and any $ c < 1$ that any positive increasing solution $ y$ of $ y'' - {q^2}y = 0$ satisfies $ y(x) \geq y(0)\exp (c\int_0^x {q(t)dt)} $ on the complement of a set of finite Lebesgue measure. It is also shown that if $ \lim \inf (\int_0^x {q(t)dt/x) > 0} $ then the equation has an exponentially increasing solution and an exponentially decreasing solution.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34D05

Retrieve articles in all journals with MSC: 34D05

Additional Information

PII: S 0002-9939(1974)0344611-5
Keywords: Exponential dichotomy, monotonie solution, Riccati equation
Article copyright: © Copyright 1974 American Mathematical Society