Electron. J. Diff. Equ., Vol. 2013 (2013), No. 137, pp. 1-7.

Generalized Bohl-Perron principle for differential equations with delay in a Banach spaces

Michael Gil'

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.

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Michael Gil'
Department of Mathematics
Ben Gurion University of the Negev
P.0. Box 653, Beer-Sheva 84105, Israel
email: gilmi@bezeqint.net

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