Multiplicity results for perturbed fourth-order Kirchhoff type elliptic problems (Q470784)

It is shown that the problem \(\Delta (|\Delta u|^{p-2}\Delta u)-[M(\int_\Omega |\nabla u|^p \;dx)]^{p-1}\Delta_p u+\rho |u|^{p-2}u=\lambda f(x,u)\) in \(\Omega \), \(u=\Delta u=0\) on \(\partial \Omega \) has at least two weak solutions.