Geodesic
Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay
Archivum mathematicum, Tome 45 (2009) no. 3, pp. 223-236 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this article, stability and asymptotic properties of solutions of a real two-dimensional system $x^{\prime }(t) = \mathbf{A} (t) x(t) + \mathbf{B} (t) x (\tau (t)) + \mathbf{h} (t, x(t), x(\tau (t)))$ are studied, where $\mathbf{A}$, $\mathbf{B}$ are matrix functions, $\mathbf{h}$ is a vector function and $\tau (t) \le t$ is a nonconstant delay which is absolutely continuous and satisfies $\lim \limits _{t \rightarrow \infty } \tau (t) = \infty $. Generalization of results on stability of a two-dimensional differential system with one constant delay is obtained using the methods of complexification and Lyapunov-Krasovskii functional and some new corollaries and examples are presented.
In this article, stability and asymptotic properties of solutions of a real two-dimensional system $x^{\prime }(t) = \mathbf{A} (t) x(t) + \mathbf{B} (t) x (\tau (t)) + \mathbf{h} (t, x(t), x(\tau (t)))$ are studied, where $\mathbf{A}$, $\mathbf{B}$ are matrix functions, $\mathbf{h}$ is a vector function and $\tau (t) \le t$ is a nonconstant delay which is absolutely continuous and satisfies $\lim \limits _{t \rightarrow \infty } \tau (t) = \infty $. Generalization of results on stability of a two-dimensional differential system with one constant delay is obtained using the methods of complexification and Lyapunov-Krasovskii functional and some new corollaries and examples are presented.
Classification : 34K12, 34K20, 34K25
Keywords: stability; asymptotic behaviour; differential system; nonconstant delay; Lyapunov method 
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     title = {Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay},
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     url = {http://geodesic.mathdoc.fr/item/ARM_2009_45_3_a6/}
}
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Rebenda, Josef. Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay. Archivum mathematicum, Tome 45 (2009) no. 3, pp. 223-236. http://geodesic.mathdoc.fr/item/ARM_2009_45_3_a6/

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