Existence and uniqueness of solutions to abstract Volterra integral equations Academic Article

The existence and uniqueness of solutions to the equation u ( t ) + 0 t a ( t s ) A u ( s ) d s f ( t ) u(t) + smallint _0^ta(t - s)Au(s);ds \backepsilon f(t) , where A is a maximal monotone operator, is proved under various restrictions on A and f.