Asymptotic properties of an unstable two-dimensional differential system with delay

Josef Kalas

Asymptotic estimation of the convergence of solutions of the equation $\dot{x} (t) = b (t) x (t - τ (t))$

Josef Diblík, Denis Khusainov (2001)

Archivum Mathematicum

Similarity:

The main result of the present paper is obtaining new inequalities for solutions of scalar equation $\dot{x} (t) = b (t) x (t - τ (t))$ . Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution $x (t)$ reaches an $ε$ - neighbourhood of origin and remains in it.

Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

E. Bravyi, Robert Hakl, Alexander Lomtatidze (2002)

Czechoslovak Mathematical Journal

Similarity:

Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem $u^{'} (t) = ℓ (u) (t) + q (t), u (a) = c,$ where $ℓ C (I, ℝ) \to L (I, ℝ)$ is a linear bounded operator, $q \in L (I, ℝ)$ , and $c \in ℝ$ , are established.

Displaying similar documents to “Asymptotic properties of an unstable two-dimensional differential system with delay”

Asymptotic estimation of the convergence of solutions of the equation x ˙ ( t ) = b ( t ) x ( t - τ ( t ) )

Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

Asymptotic estimation of the convergence of solutions of the equation $\dot{x} (t) = b (t) x (t - τ (t))$