We consider the following non-linear elliptic equation Δ u + f ( x ,u ) = 0,x ∈ K on fractal domains with zero-Dirichlet boundary conditions,where K is self-similar fractal,Δ is the Laplacian defined on K. f(x,t) is asymptotically linear as t →∞ . We get the non-trivial and non-negative solution by using Mountain Pass lemma.
