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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.14408 |
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| _version_ | 1866929427922812928 |
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| author | Diwan, Ali Iaia, Joseph |
| author_facet | Diwan, Ali Iaia, Joseph |
| contents | In this paper, we study radial solutions of $Δu + K(|x|)f(u) = 0$ in the exterior of the ball of radius $R > 0$ in $\mathbb{R}^N$ with $ N > 2$ where $f$ grows superlinearly at infinity and is singular at 0 with $f \sim \frac{1}{|u|^{q-1}u}$ where $0 < q < 1.$ We also assume $ K(r) \sim |r|^{- α}$ for large $r$ and establish the existence of two infinite families of solutions when $ N + q(N-2) < α< 2(N-1).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two Infinite Families of Solutions for Singular Superlinear Equations on Exterior Domains Diwan, Ali Iaia, Joseph Analysis of PDEs In this paper, we study radial solutions of $Δu + K(|x|)f(u) = 0$ in the exterior of the ball of radius $R > 0$ in $\mathbb{R}^N$ with $ N > 2$ where $f$ grows superlinearly at infinity and is singular at 0 with $f \sim \frac{1}{|u|^{q-1}u}$ where $0 < q < 1.$ We also assume $ K(r) \sim |r|^{- α}$ for large $r$ and establish the existence of two infinite families of solutions when $ N + q(N-2) < α< 2(N-1).$ |
| title | Two Infinite Families of Solutions for Singular Superlinear Equations on Exterior Domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.14408 |