Sublinear Elliptic Equation on Fractal Domains  

作　　者：HE Zhenya 

机构地区：[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China.

出　　处：《Journal of Partial Differential Equations》2011年第2期97-113,共17页偏微分方程（英文版）

摘　　要：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 -△u=λu- a（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.

关 键 词：Self-similar fractal saddle point theorem elliptic equation mountain pass lemma Laplacian operator. 

分 类 号：O175.26[理学—数学] O175.29[理学—基础数学]