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We consider the boundary Hardy–Hénon equation
where 
\[ -\Delta u=(1-|x|)^{\alpha} u^{p},\ \ x\in B_1(0), \]
$B_1(0)\subset \mathbb {R}^{N}$
$(N\geq 3)$ is a ball of radial 
$1$ centred at 
$0$, 
$p>0$ and 
$\alpha \in \mathbb {R}$. We are concerned with the estimate, existence and nonexistence of positive solutions of the equation, in particular, the equation with Dirichlet boundary condition. For the case 
$0< p<({N+2})/({N-2})$, we establish the estimate of positive solutions. When 
$\alpha \leq -2$ and 
$p>1$, we give some conclusions with respect to nonexistence. When 
$\alpha >-2$ and 
$1< p<({N+2})/({N-2})$, we obtain the existence of positive solution for the corresponding Dirichlet problem. When 
$0< p\leq 1$ and 
$\alpha \leq -2$, we show the nonexistence of positive solutions. When 
$0< p<1$, 
$\alpha >-2$, we give some results with respect to existence and uniqueness of positive solutions.
