Journal of Inequalities and Applications
Volume 2005 (2005), Issue 1, Pages 49-65

Linear functional differential equations possessing solutions with a given growth rate

Ravi P. Agarwal1 and Andrei Rontó2,3

1Department of Mathematical Sciences, Florida Institute of Technology, 150 West University Boulevard, Melbourne 32901-6975, FL, USA
2Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkovskaya Street, Kiev 01601, Ukraine
3Mathematical Institute, Academy of Sciences of the Czech Republic, Žižkova 22, Brno 61662, Czech Republic

Received 7 April 2004

Copyright © 2005 Ravi P. Agarwal and Andrei Rontó. 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, conditions under which, for arbitrary forcing terms from a suitable class, a linear inhomogeneous functional differential equation in a preordered Banach space possesses solutions satisfying a certain growth restriction.