A System of p-Laplacian Equations on the Sierpinski Gasket

TL;DR

This paper investigates boundary value problems involving the weak p-Laplacian on the Sierpinski gasket, establishing the existence of multiple solutions under certain parameter conditions.

Contribution

It introduces a new analysis of p-Laplacian systems on fractal structures, proving the existence of multiple solutions on the Sierpinski gasket.

Findings

Existence of at least two nontrivial weak solutions for certain parameters.

Extension of p-Laplacian boundary value problems to fractal domains.

Application of variational methods to fractal differential equations.

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 $(\lambda,\gamma) \in \mathbb{R}^2.$