Multiplicity of solutions for a class of nonlocal regional elliptic equations

In this article we are interested in the nonlinear Schrödinger equation with nonlocal regional diffusion:(0.1)(−Δ)ραu+u=f(x,u) in Rn,u∈Hα(Rn), where α∈(0,1) and (−Δ)ρα is a variational version of the regional Laplacian, whose range of scope is a ball with radius ρ(x)>0. By using the symmetric mountain pass theorem and the genus properties in critical point theory, we show that problem (0.1) has infinitely many solutions. Recent results in the literature are significantly improved.