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)



Quickly oscillating solutions of autonomous ordinary differential equations

Authors: Stephen R. Bernfeld and A. Lasota
Journal: Proc. Amer. Math. Soc. 30 (1971), 519-526
MSC: Primary 34.42
MathSciNet review: 0285764
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We are concerned here with the asymptotic behavior of quickly oscillating solutions of systems of differential equations. It is shown that the limit of the norm of any quickly oscillating solution exists and is either equal to infinity or zero. We then determine asymptotic bounds on the solutions by imposing certain growth conditions on the right-hand side of the equation. Our results, when applied to second order equations, yield asymptotic behavior of both the solutions and its derivatives.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34.42

Retrieve articles in all journals with MSC: 34.42

Additional Information

Keywords: Quickly oscillating solutions, bounds on solutions, asymptotic behavior of solutions and their derivatives, zeros of solutions
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society