Remarks on two fourth order elliptic problems in whole space

Baishun Lai, Dong Ye

We are interested in entire solutions for the semilinear biharmonic equation ${\Delta }^{2}u=f(u)$ in ${\mathbb{R}}^N$, where $f(u)=e^u$ or $-u^{-p}(p>0)$. For the exponential case, we prove tha…