Journal of Inequalities and Applications
Volume 2005 (2005), Issue 3, Pages 235-250

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

Copyright © 2005 Andrei Rontó and Jiří Šremr. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.