A System of p-Laplacian Equations on the Sierpinski Gasket

In this paper we study a system of boundary value problems involving weak p-Laplacian on the Sierpi'nski gasket in ${\mathbb{R}}^2$. Parameters $\lambda, \gamma, \alpha, \beta$arerealand$1<q<p<\alpha+\beta.$Functions$a,b,h : $\mathcal{S}$ \rightarrow $\mathbb{R}$$aresuitablychosen\mathrm{.}For$p>1$ we show the existence of at least two nontrivial weak solutions to the system of equations for some $(\lambda ,\gamma )\in {\mathbb{R}}^2\mathrm{.}$