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

Robert Hakl; Alexander Lomtatidze; Bedřich Půža

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.

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.

Displaying similar documents to “New 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

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