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arXiv · 1907.00017

On a multivalued differential equation with nonlocality in time

André Eikmeier·Etienne Emmrich
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Abstract

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.

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André Eikmeier, Etienne Emmrich. 2019-06-28. On a multivalued differential equation with nonlocality in time. https://arxiv.org/abs/1907.00017

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