$L^p$ theory for a singular Sturm-Liouville equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929626717093888 |
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| author | Castro, Hernán Proaño, Iván |
| author_facet | Castro, Hernán Proaño, Iván |
| contents | In this paper we consider the following Sturm-Liouville equation \[ \left\{ \begin{aligned}
-(x^{2α}u'(x))'+u(x)&=f(x) && \text{in } (0,1],\\ u(1)&=0 \end{aligned} \right. \] where $α<1$ is a nonzero real number and $f$ belongs to $L^p(0,1)$ for $p\geq 1$. We analyze the existence and regularity of solutions under suitable weighted Dirichlet boundary condition at the origin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07875 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^p$ theory for a singular Sturm-Liouville equation Castro, Hernán Proaño, Iván Classical Analysis and ODEs 34B05, 34B08, 34B16 In this paper we consider the following Sturm-Liouville equation \[ \left\{ \begin{aligned} -(x^{2α}u'(x))'+u(x)&=f(x) && \text{in } (0,1],\\ u(1)&=0 \end{aligned} \right. \] where $α<1$ is a nonzero real number and $f$ belongs to $L^p(0,1)$ for $p\geq 1$. We analyze the existence and regularity of solutions under suitable weighted Dirichlet boundary condition at the origin. |
| title | $L^p$ theory for a singular Sturm-Liouville equation |
| topic | Classical Analysis and ODEs 34B05, 34B08, 34B16 |
| url | https://arxiv.org/abs/2412.07875 |