Properties of the extremal solution for a fourth-order elliptic problem

Baishun Lai, Zhuoran Du

Let ${\lambda }^{\ast }>0$ denote the largest possible value of $\lambda$ such that $$ \{{array}{lllllll} Δ^{2}u=\fracλ{(1-u)^{p}} & \{in}\ \ B, 0<u\leq 1 & \{in}\ \ B, u=\frac{\partial u}{\partial n…