This paper is devoted to studies of non-negative, non-trivial (classical, punctured, or distributional) solutions the higher order Hardy-H\'enon equations \[ (-\Delta)^m u = |x|^\sigma u^p \] in $\mathbf R^n$ with $p > 1$. We show that condition n - 2m \frac{2m+\sigma}{p-1} >0 necessary for existence distributional solutions. For $n \geq 2m$ and $\sigma -2m$, we prove any solution satisfies an ...
