In this paper, we consider the existence of nontrivial solutions to the
following critical biharmonic problem with a logarithmic term \begin{equation*}
\begin{cases} \Delta^2 u=\mu \Delta u+\lambda u+|u|^{2^{**}-2}u+\tau u\log u^2,
\ \ x\in\Omega, u|_{\partial \Omega }=\frac{\partial u}{\partial
n}|_{\partial\Omega}=0, \end{cases} \end{equation*} where μ,λ,τ∈R, ∣μ∣+∣τ∣=0, Δ2=ΔΔ denotes the
iterated N-dimensional Laplacian, Ω⊂RN is a bounded
domain with smooth boundary ∂Ω, 2∗∗=N−42N(N≥5)
is the critical Sobolev exponent for the embedding
H02(Ω)↪L2∗∗(Ω) and H02(Ω) is
the closure of C0∞(Ω) under the norm ∣∣u∣∣:=(∫Ω∣Δu∣2)21. The uncertainty of the sign of
slogs2 in (0,+∞) has some interest in itself. To know which of the
three terms μΔu, λu and τulogu2 has a greater
influence on the existence of nontrivial weak solutions, we prove the existence
of nontrivial weak solutions to the above problem for N≥5 under some
assumptions of λ,μ and τ