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

25 pages, 2 figures