Layered solutions for a semilinear elliptic system in a ball

We consider the following system of Schrödinger–Poisson equations in the unit ball B1B1 of R3R3:−ε2Δv+v+ωϕv−γvp=0,−Δϕ=4πωv2 with the Dirichlet boundary conditions v=ϕ=0v=ϕ=0 on ∂B1∂B1. Here ε, ω  , γ>0γ>0, v  , ϕ:B1→R, 1