Existence of a weak solution for a class of nonlinear elliptic equations on the Sierpiński gasket
UDC 517.9 We study the existence of a weak (strong) solution of the nonlinear elliptic problem\begin{gather*} -\Delta u- \lambda ug_1 +h(u)g_2=f \quad\text{in}\quad V\setminus V_0,\\u=0 \quad\text{on}\quad V_0,\end{gather*} where $V$ is a Sierpi\'nski gasket in $\mathbb{R}^{N-1},$ $N\...
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| Datum: | 2022 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6248 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.9
We study the existence of a weak (strong) solution of the nonlinear elliptic problem\begin{gather*} -\Delta u- \lambda ug_1 +h(u)g_2=f \quad\text{in}\quad V\setminus V_0,\\u=0 \quad\text{on}\quad V_0,\end{gather*} where $V$ is a Sierpi\'nski gasket in $\mathbb{R}^{N-1},$ $N\geq 2,$ $V_0$ is its boundary (consisting of $N$ its corners), and $\lambda$ is a real parameter. Here, $f,g_1,g_2\colon V\to\mathbb{R}$ and $h\colon \mathbb{R}\to\mathbb{R}$ are functions satisfying suitable hypotheses. |
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| DOI: | 10.37863/umzh.v74i10.6248 |