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)



Oscillation of linear second-order differential systems

Authors: Man Kam Kwong, Hans G. Kaper, Kazuo Akiyama and Angelo B. Mingarelli
Journal: Proc. Amer. Math. Soc. 91 (1984), 85-91
MSC: Primary 34C10
MathSciNet review: 735570
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This article is concerned with the oscillatory behavior at infinity of the solution $ y:[a,\infty ) \to {{\mathbf{R}}^n}$ of a system of second-order differential equations, $ y''\left( t \right) + Q\left( t \right)y\left( t \right) = 0$, $ t \in [a,\infty )$; $ Q$ is a continuous matrix-valued function on $ [a,\infty )$ whose values are real symmetric matrices of order $ n$; it is assumed that the largest eigenvalue of the matrix $ \int_a^t {Q\left( s \right)ds} $ tends to infinity as $ t \to \infty $. Various sufficient conditions are given which guarantee oscillatory behavior at infinity; these conditions generalize those of Mingarelli [C.R. Math. Rep. Acad. Sci. Canada 2 (1980), 287-290, and Proc. Amer. Math. Soc. 82 (1981), 593-598].

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

Similar Articles

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

Retrieve articles in all journals with MSC: 34C10

Additional Information

Keywords: Matrix differential equation, oscillation theory, matrix Riccati equation, Riccati inequality
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society