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

Josef Kalas

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 $\dot{x} (t) = b (t) x (t - τ (t))$

Josef Diblík, Denis Khusainov (2001)

Archivum Mathematicum

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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

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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.

A note on the Cauchy problem for first order linear differential equations with a deviating argument

Robert Hakl, Alexander Lomtatidze (2002)

Archivum Mathematicum

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Conditions for the existence and uniqueness of a solution of the Cauchy problem $u^{'} (t) = p (t) u (τ (t)) + q (t), u (a) = c,$ established in [2], are formulated more precisely and refined for the special case, where the function $τ$ maps the interval $] a, b [$ into some subinterval $[τ_{0}, τ_{1}] \subseteq [a, b]$ , which can be degenerated to a point.

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

A note on the Cauchy problem for first order linear differential equations with a deviating argument

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