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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-1984-0735570-8
MathSciNet review: 735570
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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].


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DOI: https://doi.org/10.1090/S0002-9939-1984-0735570-8
Keywords: Matrix differential equation, oscillation theory, matrix Riccati equation, Riccati inequality
Article copyright: © Copyright 1984 American Mathematical Society