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A System of Time-Dependent Hemivariational Inequalities with Volterra Integral Terms

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Abstract

In this paper, we consider a system of time-dependent hemivariational inequalities with Volterra integral terms by using a surjectivity theorem for pseudomonotone operators and the Banach fixed point theorem, rather than the Knaster-Kuratowski-Mazurkiewicz theorems used by many researchers in recent literature for systems of hemivariational inequalities. Under some suitable conditions, the existence and uniqueness result of solution to the problem considered is obtained by proving that a derived vector inclusion problem with Volterra integral term is solvable.

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Acknowledgments

We are grateful to two anonymous referees for their valuable comments and suggestions leading to the improvement of this paper. This work was supported by the National Natural Science Foundation of China (11101069, 11171237) and China Postdoctoral Science Foundation (2014M552328).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Yi-bin Xiao

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Nan-jing Huang & Jue Lu

  3. School of Mathematics, Physics and Information Science, The University of Shaoxing, Shaoxing, 312000, Zhejiang, People’s Republic of China

    Jue Lu

Authors
  1. Yi-bin Xiao
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  2. Nan-jing Huang
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  3. Jue Lu
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Correspondence to Yi-bin Xiao.

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Xiao, Yb., Huang, Nj. & Lu, J. A System of Time-Dependent Hemivariational Inequalities with Volterra Integral Terms. J Optim Theory Appl 165, 837–853 (2015). https://doi.org/10.1007/s10957-014-0602-y

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  • DOI: https://doi.org/10.1007/s10957-014-0602-y

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