On the Cauchy problem for linear hyperbolic functional-differential equations

被引：0

作者：

Alexander Lomtatidze

Jiří Šremr

机构：

[1] Academy of Sciences of the Czech Republic,Institute of Mathematics

[2] branch in Brno,undefined

来源：

Czechoslovak Mathematical Journal | 2012年 / 62卷

关键词：

functional-differential equation of hyperbolic type; Cauchy problem; Fredholm alternative; well-posedness; existence of solutions; 35L15; 35L10;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：391 / 440

页数：49

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