A multiplicity theorem for a class of nonlocal elliptic equations involving even nonlinearities

In this paper, on a bounded domain $\mathrm{\Omega }\subset {\mathbf{R}}^n$, we consider a nonlocal problem of the type \cases{-Δu=Q(u,λ)f(u) & in $Ω$ \cr & \cr u=0 & on $\partialΩ$\cr} where $Q:H_0^1(\mathrm{\Omega })\times \mathbf{R}\to \mathbf{R}$, proving, under suitable assumptions, the existence of at least three weak solutions for each $\lambda$ running in a suitable interval.