Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 1, Pages 49-65
doi:10.1155/JIA.2005.49

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

Abstract

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.