Existence of weak solutions for a fourth-order Navier boundary value problem

In this paper we discuss the existence of weak solutions for the fourth-order Navier boundary value problem { Δ 2 u ( x ) + c Δ u ( x ) = λ u ( x ) + f ( u ( x ) ) , in  Ω , u = Δ u = 0 , on  ∂ Ω , where λ is a parameter, Δ 2 is the biharmonic operator, Ω ⊂ R N ( N > 4 ) is a smooth bounded domain, and f ∈ C ( R , R ) . We use topological degree theory and critical point theory to establish the existence.