On nonlinear Volterra equations in Hilbert spaces (Q1194554)

The author proves the existence of a solution for the Volterra integral equation \(A(t)u(t)+\int^ t_ 0a(t-s)B(s)u(s)ds+\int^ t_ 0C(s)u(s)ds\ni f(t)\), \(0<t<\infty\), where \(u(\cdot)\) belongs to a real reflexive Banach space, \(a(\cdot)\) is a scalar function, \(A(t)\) and \(B(t)\) are subdifferentials, \(A(t)\) is not necessarily compact and \(C(t)\) is a Lipschitzian compact operator. The uniqueness problem is studied in some special cases.