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

Abstract

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 $$\cases{-K\left(\int_{\Omega}|\nabla u(x)|^2dx\right)\Delta u = h(x,u) & in $\Omega$\cr & \cr {{\partial u}\over {\partial\nu}}=0 & on $\partial\Omega$.\cr}$$