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

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.

Keywords

• Banach space
• differential equation with delay
• linear equation
• exponential stability