(untitled) (Journal of Partial Differential Equations, 2011)
This paper investigates sub-linear elliptic equations on self-similar fractal sets. With an appropriately defined Laplacian, we obtain the existence of nontrivial solutions of sub-linear elliptic equations -Δu=λu-α(x)|u|^q-1u-f(x,u), with zero boundary Dirichlet conditions. The results are obtained by using Mountain Pass Lemma and Saddle Point Theorem.