Non-linear elliptic equations on fractal domain

We consider the following non-linear elliptic equation 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. Biography: HE Zhenya(1971–), male, Ph.D. candidate, research direction: analysis on fractal.