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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.24268 |
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| _version_ | 1866911183506767872 |
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| author | Wang, Xu-Jia Zhang, Xinyue |
| author_facet | Wang, Xu-Jia Zhang, Xinyue |
| contents | We introduce a new minimax principle to prove the existence of multi-peak solutions to the Neumann problem of the $p$-Laplace equation $$ -\varepsilon^p Δ_p u = u^{q-1} - u^{p-1} \ \ \text{in}\ Ω,$$ where $\Om$ is a bounded domain in $\mathbb{R}^n$ with smooth boundary, $1<p<n$ and $p<q< \frac{np}{n-p}$. The minimax principle will be applied to the set of peak functions, which is a subset of the Sobolev space $W^{1,p} (Ω)$. The argument is based on a combination of variational method, topological degree theory, and gradient flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new minimax principle and application to the p-Laplace equation Wang, Xu-Jia Zhang, Xinyue Analysis of PDEs We introduce a new minimax principle to prove the existence of multi-peak solutions to the Neumann problem of the $p$-Laplace equation $$ -\varepsilon^p Δ_p u = u^{q-1} - u^{p-1} \ \ \text{in}\ Ω,$$ where $\Om$ is a bounded domain in $\mathbb{R}^n$ with smooth boundary, $1<p<n$ and $p<q< \frac{np}{n-p}$. The minimax principle will be applied to the set of peak functions, which is a subset of the Sobolev space $W^{1,p} (Ω)$. The argument is based on a combination of variational method, topological degree theory, and gradient flow. |
| title | A new minimax principle and application to the p-Laplace equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.24268 |