Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 137, pp. 1-7.

Title: Generalized Bohl-Perron principle for differential equations
       with delay in a Banach spaces
        
Author: Michael  Gil' (Ben Gurion Univ., of the Negev, Israel)

Abstract:
 We consider a linear homogeneous functional differential equation
 with delay in a Banach space.  It is proved that if the corresponding 
 non-homogeneous equation,  with an arbitrary free term bounded on 
 the positive half-line  and with the zero initial condition, 
 has a bounded solution,  then the considered homogeneous equation 
 is exponentially  stable. 

Submitted  February 27, 2013. Published June 20, 2013.
Math Subject Classifications: 34K30, 34K06, 34K20.
Key Words: Banach space; differential equation with delay;
           linear  equation; exponential stability.