On a multivalued differential equation with nonlocality in time
Analysis of PDEs
2019-07-02 v1
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.
Cite
@article{arxiv.1907.00017,
title = {On a multivalued differential equation with nonlocality in time},
author = {André Eikmeier and Etienne Emmrich},
journal= {arXiv preprint arXiv:1907.00017},
year = {2019}
}