Abstract
Let $\mathcal{S}$ be the Sierpi\’nski
gasket in $\mathbb{R}^2$ and
$\mathcal{S}_{0}$ denote the boundary of
$\mathcal{S}$. In this paper, we study the following
non-homogeneous $p$-Laplacian equation \begin{align*}
-\Delta_p u &= \lambda
|u|^{q-2} u + f
\text{~in}\;
\mathcal{S}\setminus\mathcal{S}_0\\
u &=
0\;\mbox{~on}\;
\mathcal{S}_0, \end{align*} where
$p$, $q$, $\lambda$ are real numbers such that
$\lambda >0$, $1
, 
