  In this paper we study the following boundary value problem involving the
weak p-Laplacian. \begin{equation*} \quad -M(\|u\|_{\mathcal{E}_p}^p)\Delta_p u
= h(x,u) \; \text{in}\; \mathcal{S}\setminus\mathcal{S}_0; \quad u = 0 \;
\mbox{on}\; \mathcal{S}_0, \end{equation*} where $\mathcal{S}$ is the
Sierpi\'nski gasket in $\mathbb{R}^2$, $\mathcal{S}_0$ is its boundary. $M :
\mathbb{R} \to \mathbb{R}$ defined by $M(t) = at^k +b$ and $a,b,k >0$ and $h :
\mathcal{S} \times \mathbb{R} \to \mathbb{R}.$ We will show the existence of
two nontrivial weak solutions to the above problem.
