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Existence of multiple solutions of a p-Laplacian equation on the Sierpinski Gasket. (arXiv:1807.06887v1 [math.AP])
来源于:arXiv
In this paper we study the following boundary value problem involving the
weak p-Laplacian. \begin{equation*}
\quad -M(\|u\|_{\mathcal{E}_p}^p)\Delta_p u = h(x,u) \; \text{in}\;
\mathcal{S}\setminus\mathcal{S}_0; \quad u = 0 \; \mbox{on}\; \mathcal{S}_0,
\end{equation*} where $\mathcal{S}$ is the Sierpi\'nski gasket in
$\mathbb{R}^2$, $\mathcal{S}_0$ is its boundary. $M : \mathbb{R} \to
\mathbb{R}$ defined by $M(t) = at^k +b$ and $a,b,k >0$ and $h : \mathcal{S}
\times \mathbb{R} \to \mathbb{R}.$ We will show the existence of two nontrivial
weak solutions to the above problem. 查看全文>>