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Existence of solution to a Dirichlet elliptic problem on the Sierpi´nski gasket
  • Arun Kumar Badajena,
  • Rasmita Kar
Arun Kumar Badajena
NIT Rourkela
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Rasmita Kar
NIT Rourkela
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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.