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Journal of Convex Analysis 27 (2020), No. 2, 423--442
Copyright Heldermann Verlag 2020

Stability Analysis of Partial Differential Set-Valued Variational Inequalities on Banach Spaces

Wei Li
Geomathematics Key Laboratory, Chengdu University of Technology, Chengdu 610059, P.R. China

Xianfu Wang
Dept. of Mathematics, University of British Columbia, Kelowna B.C., Canada V1V~1V7

We consider the partial differential set-valued variational inequality (PDSVI) on real Banach spaces. We give conditions for the existence and uniqueness of mild solution of the PDSVI, and establish closedness and continuity of the mild solution set mapping of the PDSVI. The proofs of the main results are based on the theory of semigroups, set-valued mappings, and variational inequality.

Keywords: Partial differential set-valued variational inequality, stability, mild solution, continuity.

MSC: 49J40, 47J20, 49J53.

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