Classification of the stable solution to biharmonic problems in large   dimensions
  We give a new bound on the exponent for the nonexistence of stable solutions to the biharmonic problem $$\Delta^2u=u^p,\quad u>0 in \mathbb{R}^n $$ where $p>1, n \geq 20$. 
Juncheng Wei, Xingwang Xu and Wen Yang
math.AP math.FA