Sublinear Elliptic Equation on Fractal Domains (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  $-Δu=λu-α(x)|u|^{q-1}u-f(x,u)$,  with zero boundary Dirichlet conditions. The results are obtained by using Mountain Pass Lemma and Saddle Point Theorem.
Keywords: Self-similar fractal; saddle point theorem; elliptic equation; mountain pass lemma; Laplacian operator