Well-posedness of a class of generalized mixed hemivariational–variational inequalities. (August 2019)

• Record Type: Journal Article
• Authors: Bai, Yunru; Migórski, Stanisław; Zeng, Shengda
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 424
• Page End: 444
• Publication Date: 2019-08
• Subjects: Mixed hemivariational–variational inequality -- Fixed point theory -- Subdifferential operator -- Ladyzhenskaya–Babǔska–Brezzi (LBB) condition -- Frictional contact problem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.02.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The purpose of this paper is to investigate a class of generalized mixed hemivariational–variational inequalities of elliptic type in a Banach space. A well-posedness result for the inequality is obtained, including existence, uniqueness, and stability of solution. The approach is based on a set-valued fixed point theorem combined with the theory of nonsmooth analysis. An elastic contact problem with the constitutive law involving a convex subdifferential inclusion is considered as an illustrative application, in which the contact boundary conditions are described by a unilateral frictionless contact condition, and a bilateral multivalued frictional contact law.