We consider a family of polyharmonic problems of the form
(−Δ)mu=g(x,u) in Ω, Dαu=0 on ∂Ω, where Ω⊂ℝn is a bounded domain, g(x,⋅)∈L∞(Ω), and
|α|<m. By using the fibering method, we obtain some results about the existence of solution and its multiplicity under certain assumptions on
g. We also consider a family of biharmonic problems of the form
Δ2u+(Δϕ+|∇ϕ|2)Δu+2∇ϕ⋅∇Δu=g(x,u), where ϕ∈C2(Ω¯), and Ω, g, and the boundary condition are the same as above. For this problem, we prove the existence and multiplicity of solutions too.