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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Stability of solutions of linear delay differential equations


Authors: M. R. S. Kulenović, G. Ladas and A. Meimaridou
Journal: Proc. Amer. Math. Soc. 100 (1987), 433-441
MSC: Primary 34K20; Secondary 34D05, 34K25
DOI: https://doi.org/10.1090/S0002-9939-1987-0891141-7
MathSciNet review: 891141
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Abstract: Consider the linear differential equation

$\displaystyle (1)\quad \dot x(t) = \sum\limits_{i = 1}^n {{p_i}(t)x(t - {\tau _i})} = 0,\quad t \geqslant {t_0},$

where $ {p_i} \in C([{t_0},\infty ),{\mathbf{R}})$ and $ {\tau _i} \geqslant 0$ for $ i = 1,2, \ldots ,n$. By investigating the asymptotic behavior first of the nonoscillatory solutions of (1) and then of the oscillatory solutions we are led to new sufficient conditions for the asymptotic stability of the trivial solution of (1).

When the coefficients of (1) are all of the same sign, we obtain a comparison result which shows that the nonoscillatory solutions of (1) dominate the growth of the oscillatory solutions.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0891141-7
Keywords: Linear delay differential equations, stability of solutions, asymptotically stable
Article copyright: © Copyright 1987 American Mathematical Society