Abstract : Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent:

(P_{λ}){<K1.1/>┊

<K1.1 ilk="MATRIX" >
Δ²u-(a∫_{Ω}|∇u|²dx+b)Δu+cu=f(x)|u|^{-γ}-λ|u|^{p-2}u in Ω,
Δu=u=0 on ∂Ω.
</K1.1>
where Ω is a smooth bounded domain of ℝⁿ (n≥5), Δ² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0<γ<1, λ>0, 0<p≤2^{♯} and a,b,c are three positive constants with a+b>0 and f belongs to a given Lebesgue space.