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.