The multiplicity of nontrivial solutions for hemivariational inequalities involving nonlocal elliptic operators. (February 2015)

• Record Type: Journal Article
• Authors: Xi, Lijing; Huang, Yisheng; Zhou, Yuying
• Is Part Of: Nonlinear analysis. Volume 21(2015)
• Page Start: 87
• Page End: 98
• Publication Date: 2015-02
• Subjects: Nonlocal elliptic operators -- Local Lipschitz function -- Palais–Smale condition -- Multiple solutions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.06.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In the paper, we consider the following hemivariational inequality driven by nonlocal operators of elliptic type: { − L K u ∈ λ ∂ F ( x, u ) + μ ∂ G ( x, u ) in Ω u = 0 in R n ∖ Ω, where Ω is a smoothly bounded domain in R n and λ, μ ∈ R are two positive parameters. By using nonsmooth critical point theory, we obtain two multiplicity theorems, in which we guarantee that the hemivariational inequality problems produce at least two nontrivial solutions. Moreover, some properties of solutions are also given.