Displaying similar documents to “Abstract differential inequalities and the Cauchy problem for infinite-dimensional linear functional differential equations.”

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 ] ⊆ [ a , b ] , which can be degenerated to a point.

On the Cauchy problem for linear hyperbolic functional-differential equations

Alexander Lomtatidze, Jiří Šremr (2012)

Czechoslovak Mathematical Journal

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We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption...