Causal functional differential equations in Banach spaces (Q960236)

The author considers the Cauchy problem \[ u'(t)= (Qu)(t)\quad\text{a.e. }t\in [0, b), \] \[ u|_{[-\sigma,0]}= \varphi\in C_\sigma, \] where \(Q\) is a causal operator with prescribed conditions, \(C_\sigma= C([-\sigma, 0]; E)\) and \(E\) is a real separable Banach space. Existence results are given and some topological properties of solution sets are obtained. An example of a Volterra integro-differential equation with delay is presented.