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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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.
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
- Hemivariational inequality
- KKM mapping
- Tikhonov regularization
- Coercivity condition
Mathematics Subject Classification (2010)