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On the Cauchy problem for linear hyperbolic functional-differential equations

Alexander LomtatidzeJiří Šremr — 2012

Czechoslovak Mathematical Journal

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 in the existing...

On an antiperiodic type boundary value problem for first order linear functional differential equations

Robert HaklAlexander LomtatidzeJiří Šremr — 2002

Archivum Mathematicum

Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem u ' ( t ) = ( u ) ( t ) + q ( t ) , u ( a ) + λ u ( b ) = c are established, where : C ( [ a , b ] ; R ) L ( [ a , b ] ; R ) is a linear bounded operator, q L ( [ a , b ] ; R ) , λ R + , and c R . The question on the dimension of the solution space of the homogeneous problem u ' ( t ) = ( u ) ( t ) , u ( a ) + λ u ( b ) = 0 is discussed as well.

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