Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 3, Pages 235-250
doi:10.1155/JIA.2005.235

Abstract differential inequalities and the Cauchy problem for infinite-dimensional linear functional differential equations

Andrei Rontó1,2 and Jiří Šremr2

 1Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkovskaya, Kiev 01601, Ukraine
2Mathematical Institute, Czech Academy of Sciences, Žižkova 22, Brno 61662, Czech Republic
Received 27 August 2003; Revised 18 November 2003

Abstract

We establish optimal, in a sense, unique solvability conditions of the Cauchy problem for a wide class of linear functional differential equations in a Banach space with a solid wedge. The conditions are formulated in terms of certain abstract functional differential inequalities.