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Asymptotic estimation of the convergence of solutions of the equation $$\dot x(t)=b(t) x(t-\tau (t))$$. (English) Zbl 1090.34059
Summary: The main result of the paper is to obtain new inequalities for solutions of scalar equation $$\dot x(t)= b(t)x(t-\tau (t))$$. Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution $$x(t)$$ reaches as $$\varepsilon$$ - neighbourhood of origin and remains in it.
MSC:
 34K20 Stability theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations
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