A System of p-Laplacian Equations on the Sierpinski Gasket

Abstract

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 $\lambda, \gamma, \alpha, \beta$ are real and $1<q<p<\alpha+\beta.$ Functions $a,b,h : \mathcal{S} \rightarrow \mathbb{R}$ are suitably chosen. For $p>1$ we show the existence of at least two nontrivial weak solutions to the system of equations for some $(\lambda,\gamma) \in \mathbb{R}^2.$