MMN-2913
General history-dependent operators with applications to differential equations
- Xiuwen Li,
Guangxi University for Nationalities, Faculty of Mathematics and Physics, Nanning 530006, P.R. China,
liux@cs.fsu.edu - Biao Zeng,
Guangxi University for Nationalities, Faculty of Mathematics and Physics, Nanning 530006, P.R. China,
biao.zeng@outlook.com
Abstract
In this paper, we introduce a class of nonlinear operators--the class of general history-dependent operators. These are the operators defined on spaces of functions endowed with a structure of Banach space (the case of bounded interval of time) or Fr\'{e}chet space (the case of unbounded interval of time). We state and prove various properties of such operators, including fixed point properties. Moreover, we also study several classes of differential equations in Banach spaces, for which we our previous results can be applied.
Vol. 23 (2022), No. 1, pp. 327-337
DOI: 10.18514/MMN.2022.2913