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 {Δ2u(x)+cΔu(x)=λu(x)+f(u(x)),in  Ω,u=Δu=0,on  ∂Ω, where λλ is a parameter, Δ2Δ2 is the biharmonic operator, Ω⊂RN(N>4)Ω⊂RN(N>4) is a smooth bounded domain, and f∈C(R,R)f∈C(R,R). We use topological degree theory and critical point theory to establish the existence.