In this paper we study the existence of solutions for differential equations with state dependent delay on an unbounded domain. Our results are based on the properties of the Kuratowski measure of noncompactness and Darbo's fixed point theorem.
"Functional Differential Equations with State-Dependent Delay on Unbounded Domains in a Banach Space." Commun. Math. Anal. 12 (2) 85 - 101, 2012.