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Uniqueness and Hyers-Ulam Stability of Random Differential Variational Inequalities with Nonlocal Boundary Conditions

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Abstract

In this paper, we consider a new class of random differential variational inequalities (RDVIs) with nonlocal boundary conditions in Hilbert spaces. We apply the projection operator, Gronwall’s lemma and a result on the existence of a random differential inclusion to establish uniqueness and Hyers–Ulam stability results of the abstract inequality. As an illustrative application, the linear random differential complementarity systems and a price control model are investigated.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (11661030, 11961014), Natural Science Foundation of Guangxi Province (2018GXNSFAA281021) and Technology Base Foundation of of Guangxi Province (AD20159017), and the Foundation of Guilin University of Technology (GUTQDJJ2017062). The authors are grateful to the editor and the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. College of Science, Guilin University of Technology, Guilin, 541004, Guangxi, People’s Republic of China

    Yirong Jiang & Qiongfen Zhang

  2. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, 041004, People’s Republic of China

    Qiqing Song

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  1. Yirong Jiang
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  2. Qiqing Song
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  3. Qiongfen Zhang
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Correspondence to Yirong Jiang.

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Communicated by Lorenz Biegler.

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Jiang, Y., Song, Q. & Zhang, Q. Uniqueness and Hyers-Ulam Stability of Random Differential Variational Inequalities with Nonlocal Boundary Conditions. J Optim Theory Appl 189, 646–665 (2021). https://doi.org/10.1007/s10957-021-01850-x

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