Multiplicity Results for the Nonlinear Weighted Laplacian Equation on the Sierpiński Gasket

Abstract

Abstract We study a Dirichlet problem driven by a weighted Laplacian on the Sierpinski gasket. Under suitable growth assumptions on the nonlinear term, we establish existence and multiplicity results by means of direct minimization, the mountain-pass theorem, and an abstract two-critical-point result for Szulkin-type functionals.