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.