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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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