The multiplicity of nontrivial solutions for hemivariational inequalities involving nonlocal elliptic operators

In the paper, we consider the following hemivariational inequality driven by nonlocal operators of elliptic type: {−LKu∈λ∂F(x,u)+μ∂G(x,u)in  Ωu=0in  Rn∖Ω, where ΩΩ is a smoothly bounded domain in RnRn and λ,μ∈Rλ,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.