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.
|Journal||Electronic Journal of Differential Equations|
|State||Published - 20 Jun 2013|
- Banach space
- Differential equation with delay
- Exponential stability
- Linear equation
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