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)
