Abstract
We study the existence of a weak (strong) solution of the nonlinear
elliptic problem \begin{equation*}
\begin{gathered} -\Delta u-
\lambda ug_1 +h(u)g_2=f
\quad\text{in }
V\setminus V_0\\ u=0
\quad\text{on } V_0,
\end{gathered}\end{equation*} where
\small{$V$} is the Sierpi\’nski gasket
in
\small{$\mathbb{R}^{N-1}(N\geq
2)$, $V_0$} is its boundary (consisting of its
\small{$N$} corners) and $\lambda$
is a real parameter. Here,
$f,g_1,g_2:V\to\mathbb{R}$,
$h:\mathbb{R}\to\mathbb{R}$
are functions satisfying suitable hypotheses.