Let $n\geq 3$, $K$ is a bounded function in $\mathbb{R}^n$. If $u$ is a nonegative solution but equal to 0 of $$-\Delta u=Ku^{\frac{n+2}{n-2}}\quad \text{in }\,\mathbb{R}^n.$$ Can we use the strong maximum principle to deduce $u$ is positive in $\mathbb{R}^n$? I saw the strong maximum principle in the bounded domain, what about the entire space like $\mathbb{R}^n$?

Let $n\geq 3$, $K$ is a bounded function in $\mathbb{R}^n$. If $u$ is a nonegative solution but not equal to 0 of $$-\Delta u=Ku^{\frac{n+2}{n-2}}\quad \text{in }\,\mathbb{R}^n.$$ Can we use the strong maximum principle to deduce $u$ is positive in $\mathbb{R}^n$? I saw the strong maximum principle in the bounded domain, what about the entire space like $\mathbb{R}^n$?

Let $n\geq 3$, $K$ is a bounded function in $\mathbb{R}^n$. If $u$ is a nonegative solution of $$-\Delta u=Ku^{\frac{n+2}{n-2}}\quad \text{in }\,\mathbb{R}^n.$$ Can we use the strong maximum principle to deduce $u$ is positive in $\mathbb{R}^n$? I saw the strong maximum principle in the bounded domain, what about the entire space like $\mathbb{R}^n$?

Let $n\geq 3$, $K$ is a bounded function in $\mathbb{R}^n$. If $u$ is a nonegative solution but equal to 0 of $$-\Delta u=Ku^{\frac{n+2}{n-2}}\quad \text{in }\,\mathbb{R}^n.$$ Can we use the strong maximum principle to deduce $u$ is positive in $\mathbb{R}^n$? I saw the strong maximum principle in the bounded domain, what about the entire space like $\mathbb{R}^n$?

Let $n\geq 3$, $K$ is a bounded function in $\mathbb{R}^n$. If $u$ is a nonegative solution of $$-\Delta u=Ku^{\frac{n+2}{n-2}}\quad \text{in }\,\mathbb{R}^n.$$ Can we use the strong maximum principle to deduce $u$ is positive in $\mathbb{R}^n$？I saw the strong maximum pricinple in the bounded domain, what about the entire space like $\mathbb{R}^n$？Thanks for any help.

Let $n\geq 3$, $K$ is a bounded function in $\mathbb{R}^n$. If $u$ is a nonegative solution of $$-\Delta u=Ku^{\frac{n+2}{n-2}}\quad \text{in }\,\mathbb{R}^n.$$ Can we use the strong maximum principle to deduce $u$ is positive in $\mathbb{R}^n$? I saw the strong maximum principle in the bounded domain, what about the entire space like $\mathbb{R}^n$?