Geodesic
On the Cauchy problem for linear hyperbolic functional-differential equations
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 391-440.

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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 in the existing literature.
DOI : 10.1007/s10587-012-0037-2
Classification : 35A01, 35A02, 35B30, 35L10, 35L15
Keywords: functional-differential equation of hyperbolic type; Cauchy problem; Fredholm alternative; well-posedness; existence of solutions 
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     title = {On the {Cauchy} problem for linear hyperbolic functional-differential equations},
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Lomtatidze, Alexander; Šremr, Jiří. On the Cauchy problem for linear hyperbolic functional-differential equations. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 391-440. doi : 10.1007/s10587-012-0037-2. http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0037-2/

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