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Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay. (English) Zbl 1212.34235
Summary: Stability and asymptotic properties of solutions of the real two-dimensional system $x'(t) = \mathbf A (t) x(t) + \mathbf B (t) x (\tau (t)) + \mathbf h (t, x(t), x(\tau (t)))$ are studied, where $$\mathbf A$$, $$\mathbf B$$ are matrix functions, $$\mathbf h$$ is a vector function and $$\tau (t) \leq t$$ is a nonconstant delay which is absolutely continuous and satisfies $$\lim _{t \to \infty } \tau (t) = \infty$$. Generalization of results on stability of a two-dimensional differential system with one constant delay is obtained by using the methods of complexification and Lyapunov-Krasovskii functional.

##### MSC:
 34K25 Asymptotic theory of functional-differential equations 34K20 Stability theory of functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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