TY - JOUR
T1 - Sublinear Elliptic Equation on Fractal Domains
AU - Zhenya He 
JO - Journal of Partial Differential Equations
VL - 2
SP - 97
EP - 113
PY - 2011
DA - 2011/05
SN - 24
DO - http://doi.org/10.4208/jpde.v24.n2.1
UR - https://global-sci.org/intro/article_detail/jpde/5200.html
KW - Self-similar fractal
KW - saddle point theorem
KW - elliptic equation
KW - mountain pass lemma
KW - Laplacian operator
AB - <p>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&nbsp; $-Δu=λu-α(x)|u|^{q-1}u-f(x,u)$, &nbsp;with zero boundary Dirichlet conditions. The results are obtained by using Mountain Pass Lemma and Saddle Point Theorem.</p>