Critical growth biharmonic elliptic problems under Steklov-type boundary conditions

We study the fourth-order nonlinear critical problem $\Delta^2 u = u^{2*−1}$ in a smooth, bounded domain $\Omega\subset R^n$, $n\geq 5$, subject to the boundary conditions $u = \Delta u − d u_{\nu}= 0$ on $\partial \Omega$. We provide estimates for the range of parameters $d\in R$ for which this problem admits a positive solution. If the domain is the unit ball, we obtain an almost complete description.