Asymptotic estimation of the convergence of solutions of the equation \(\dot x(t)=b(t) x(t-\tau (t))\). (English) Zbl 1090.34059

Diblík, Josef; Khusainov, Denys

Arch. Math., Brno 37, No. 4, 279-287 (2001).

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

Keywords:

stability of trivial solution; estimation of convergence of nontrivial solutions