Existence results for nonlinear elliptic problems on fractal domains
  Some existence results for a parametric Dirichlet problem defined on the Sierpi\'nski fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well determined open interval of positive eigenvalues for which the problem admits at least one non-trivial weak solution. 
Massimiliano Ferrara, Giovanni Molica Bisci and Du\v{s}an Repov\v{s}
math.AP