On stable solutions of biharmonic problem with polynomial growth

Hatem Hajlaoui, Abdelaziz Harrabi, Dong Ye

We prove the nonexistence of smooth stable solution to the biharmonic problem ${\Delta }^{2}u=u^p$, $u>0$ in ${\mathbb{R}}^N$ for $1<p<\infty$ and $N<2(1+x_0)$, where $x_0$ is the largest ro…