Multiplicity Results for the Nonlinear Weighted Laplacian Equation on the Sierpi\'nski Gasket

In this paper we consider the Dirichlet boundary value problem driven by the weighted Laplacian equation and considered on the Sierpi\'nski gasket. Under suitable growth conditions imposed on the nonlinear term, we provide existence and multiplicity results employing the direct method, mountain pass theorem and some related multiplicity result.