Relationships between BC-S. D. \(\Omega(f)\) and \((K,\rho)\)-S. D. \(\Omega(f)\) in an abstract functional differential equation with infinite delay (Q2761887)

The author of this interesting paper investigates functional-differential equations of the form \(dx/dt=Ax(t)+f(t,x_t)\), where \(x_t\) is defined by \(x_t(s)=x(t+s)\) for \(t\in \mathbb{R}^-\) in a fading memory space \(B\). In order to obtain the existence of a solution to the considered problem, the author considers a certain stability property, which is referred to as \(BC\)-stability under disturbances from hull. This stability implies \(\rho \)-stability under disturbances from hull with respect to a compact set \(K\).