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Nonoscillatory Solutions of x(m) = (-1)mQ(t)x

Published online by Cambridge University Press:  20 November 2018

Sui-Sun Cheng
Sui-Sun Cheng*
Affiliation:
Department of Mathematics National Tsing Hua University Hsinchu, Taiwan300
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Abstract

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A continuous real vector function is said to be nonoscillatory on an interval if at least one of its components is of constant positive or negative sign there. In this note, various existence criteria for nonoscillatory solutions of the system x(m) = (-l)mQ(t)x are established. In some cases, additional monotonicity properties for these solutions are also given.

Keywords

34C10Nonoscillatory solutionsIndecomposable matricesComparison theorem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 1 , 01 March 1979 , pp. 17 - 21
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Hartman, P. and Wintner, A., Linear differential and difference equations with monotone solutions, Amer. J. Math. 75 (1953), 731-743.Google Scholar
2. Jones, G. and Ramkin, S. III, Oscillation properties of certain self-adjoint differential equations of the fourth order, Pacific J. Math., 63 (1976), 179-184.Google Scholar
3. Kim, W. J., Monotone and oscillatory solutions of y(n) + py = 0, Proc. AMS, 62 (1977), 77-82.Google Scholar
4. Marcus, M. and Mine, H., A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, (1964).Google Scholar
5. Read, T. T., Growth and decay of solutions of y(2n)-py = 0, Proc. AMS, 43 (1974), 127-132.Google Scholar