Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Wei Li

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

lovelylw@126.com

Xianfu Wang

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

shawn.wang@ubc.ca

Keywords

  • Partial differential set-valued variational inequality
  • stability
  • mild solution
  • continuity

Mathematics Subject Classification

49J40, 47J20, 49J53

Suggested citation

W. Li, X. Wang. “Stability Analysis of Partial Differential Set-Valued Variational Inequalities on Banach Spaces.” Journal of Convex Analysis 27 (2020), No. 2, 423–442. https://doi.org/10.68381/jca27024

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press.