One-parameter Dirichlet problems on the Sierpinski gasket

Using a three-critical-point theorem due to Arcoya and Carmona, we show that, under suitable conditions and for sufficiently large real parameters λ, the following nonlinear elliptic equation defined on the Sierpinski gasket and with zero Dirichlet boundary conditions-Δu(x)+b(x)u(x)=λf(x,u(x))has at least two nonzero weak solutions.