  The initial value problem for a multivalued differential equation is studied,
which is governed by the sum of a monotone, hemicontinuous, coercive operator
fulfilling a certain growth condition and a Volterra integral operator in time
of convolution type with exponential decay. The two operators act on different
Banach spaces where one is not embedded in the other. The set-valued right-hand
side is measurable and satisfies certain continuity and growth conditions.
Existence of a solution is shown via a generalisation of the Kakutani
fixed-point theorem.

Analysis of PDEs