# Nonlinear problems on the Sierpi\'nski gasket

## TL;DR

This paper investigates elliptic equations on fractal domains, specifically the Sierpiński gasket, using variational methods to establish the existence of multiple solutions and improve classical results in fractal analysis.

## Contribution

It introduces new existence results for solutions of nonlinear elliptic equations on fractals, extending classical variational techniques to fractal settings.

## Key findings

- Proved existence of at least two solutions for elliptic equations on the Sierpiński gasket.
- Extended the Mountain Pass Theorem application to fractal domains.
- Improved classical results by Falconer and Hu (1999) in the fractal context.

## Abstract

This paper concerns with a class of elliptic equations on fractal domains depending on a real parameter. Our approach is based on variational methods. More precisely, the existence of at least two non-trivial weak (strong) solutions for the treated problem is obtained exploiting a local minimum theorem for differentiable functionals defined on reflexive Banach spaces. A special case of the main result improves a classical application of the Mountain Pass Theorem in the fractal setting, given by Falconer and Hu (1999).