A note on multiple solutions for Kirchhoff-type equations with a Neumann condition

Using as a main tool our recent result on the strict minimax inequality proved in [5], in this note we establish a multiplicity theorem for a problem of the type \cases{-K\left(\int_Ω|\nabla u(x)|^2dx\right)Δu = h(x,u) & in $Ω$\cr & \cr {{\partial u}\over {\partialν}}=0 & on $\partialΩ$.\cr}