If $u_1\geq 0$ and $u_1\neq 0$, and satisfies $$-\Delta u_1=|u_1|^{\frac{4}{n-2}} u_1\quad \text { on }\, \mathbb{R}^n,\quad n\geq 3,$$ it follows from maximum principle that $u_1>0$. My question is: if $u_1\geq 0$ and $u_1\neq 0$, and satisfies poly-harmonic equations$$(-\Delta)^m u_1=|u_1|^{\frac{4m}{n-2m}} u_1\quad \text { on }\, \mathbb{R}^n,\quad n>2m, \quad m \geq 1, \mathbb{N}_+,$$ can we obtain $u_1>0$ like the case $m=1$？