A class of evolution differential inclusion systems

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Аннотация

The main purpose of this paper is to study an abstract system which consists of a non-linear differential inclusion with $C_0$-semigroups and history-dependent operators combined with an evolutionary non-linear inclusion involvingpseudomonotone operators, which contains several interesting problems as special cases. We first introduce a hybrid iterative system by using the Rothe method, pseudomonotone operators theory,and a feedback iterative technique. Then, the existence and a priori estimates for solutions to a series of approximating discrete problems are established. Furthermore, through a limiting procedure for solutions of the hybrid iterative system, we show that the existence of solutions to the original problem.

Об авторах

Jing Zhao

Guangxi University of Finance and Economics

Zhenhai Liu

Guangxi Minzu University; Yulin Normal University

доктор наук, профессор

Nikolaos S. Papageorgiou

Department of Mathematics, National Technical University of Athens

Email: npapg@math.ntua.gr

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© Zhao J., Liu Z., Papageorgiou N.S., 2024

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