Uniqueness of positive solutions for m-Laplacian equations with polynomial non-linearity
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912413315497984 |
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| author | Ke, Wei |
| author_facet | Ke, Wei |
| contents | We consider the uniqueness of the following positive solutions of $m$-Laplacian equation: \begin{equation} \left\{ \begin{aligned} -Δ_m u&=λu^{m-1}+u^{p-1} \quad \text{in} \quad Ω\\ u&=0 \quad \text{on} \quad \partial Ω\end{aligned} \right. \qquad(0.1)\end{equation} where $m>1$ is a constant. When $p\rightarrow m$, the uniqueness of positive solutions of $(0.1)$ is shown which is based on the essential uniqueness of first eigenfunction for $m$-Laplacian equation. Futhermore, we also prove the uniqueness results when $(0.1)$ is a perturbation of Laplacian equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15007 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniqueness of positive solutions for m-Laplacian equations with polynomial non-linearity Ke, Wei Analysis of PDEs We consider the uniqueness of the following positive solutions of $m$-Laplacian equation: \begin{equation} \left\{ \begin{aligned} -Δ_m u&=λu^{m-1}+u^{p-1} \quad \text{in} \quad Ω\\ u&=0 \quad \text{on} \quad \partial Ω\end{aligned} \right. \qquad(0.1)\end{equation} where $m>1$ is a constant. When $p\rightarrow m$, the uniqueness of positive solutions of $(0.1)$ is shown which is based on the essential uniqueness of first eigenfunction for $m$-Laplacian equation. Futhermore, we also prove the uniqueness results when $(0.1)$ is a perturbation of Laplacian equation. |
| title | Uniqueness of positive solutions for m-Laplacian equations with polynomial non-linearity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.15007 |