Existence of three solutions to a double eigenvalue problem for the p-biharmonic equation

Using a three critical points theorem and variational methods, we study the existence of at least three weak solutions of the Navier problem {Delta(vertical bar Delta u vertical bar(p-2)Delta u) - div(vertical bar del u vertical bar(p-2)del u) = lambda f(x,u) + mu g(x,u) in ohm, u = Delta u = 0 on partial derivative ohm where ohm C R-N (N >= 1) is a non-empty bounded open set with a sufficiently smooth boundary partial derivative ohm, lambda > 0, mu > 0 and f, g : ohm x R -> R are two L-1 -Caratheodory functions.