On the Existence of Solutions and Tikhonov Regularization of Hemivariational Inequality Problems

Abstract

This paper is devoted to the existence of solution and Tikhonov regularization theory for a class of hemivariational inequalities. We give the existence of solutions for the class of hemivariational inequalities when the mappings satisfy the so-called hemivariational inequality property and a rather weak coercivity condition. The existence result allows us to deduce the Tikhonov regularization result. Our results generalize some results by He (Abstr. Appl. Anal. 2012, 172061, 2012) and others.

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Funding

The first author was partially supported by National Natural Science Foundations of China (11561008), Guangxi Natural Science Foundation (2014GXNSFAA118006), and Special Fund for Guangxi Bagui Scholars (WBS 2014-04). The second author was partially supported by National Natural Science Foundations of China (71471140). The third author was partially supported by the Natural Sciences and Engineering Research Council of Canada.

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Correspondence to Xianfu Wang.

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Dedicated to Marco A. Lopez on the occasion of his 70th birthday.

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Tang, G., Wan, Z. & Wang, X. On the Existence of Solutions and Tikhonov Regularization of Hemivariational Inequality Problems. Vietnam J. Math. 48, 221–236 (2020). https://doi.org/10.1007/s10013-019-00362-6

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Keywords

  • Hemivariational inequality
  • KKM mapping
  • Tikhonov regularization
  • Existence
  • Coercivity condition

Mathematics Subject Classification (2010)

  • 90C33
  • 47J20
  • 49J40