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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2507.18662 |
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| _version_ | 1866908465287397376 |
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| author | Ahamed, Md Suzan Iaia, Joseph |
| author_facet | Ahamed, Md Suzan Iaia, Joseph |
| contents | In this paper, we prove the existence of an infinite number of radial solutions of the $p$-$Laplacian$ equation $Δ_p u + K(|x|) f(u) =0$ on the exterior of the ball of radius $R>0$ in ${\mathbb R}^{N}$ such that $u(|x|)\to 0$ as $|x|\to \infty$ where $f$ grows superlinearly at infinity and is singular at $0$ with $f(u) \sim -\frac{1}{|u|^{m-1}u}$ and $0<m<1$ for small $u$. We also assume $K(|x|) \sim |x|^{-α}$ for large $|x|$ where $N + \frac{m(N-p)}{p-1}< α<2(N-1).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of an Infinite Number of Solutions to a Singular Superlinear p-Laplacian Equation on Exterior Domains Ahamed, Md Suzan Iaia, Joseph Analysis of PDEs In this paper, we prove the existence of an infinite number of radial solutions of the $p$-$Laplacian$ equation $Δ_p u + K(|x|) f(u) =0$ on the exterior of the ball of radius $R>0$ in ${\mathbb R}^{N}$ such that $u(|x|)\to 0$ as $|x|\to \infty$ where $f$ grows superlinearly at infinity and is singular at $0$ with $f(u) \sim -\frac{1}{|u|^{m-1}u}$ and $0<m<1$ for small $u$. We also assume $K(|x|) \sim |x|^{-α}$ for large $|x|$ where $N + \frac{m(N-p)}{p-1}< α<2(N-1).$ |
| title | Existence of an Infinite Number of Solutions to a Singular Superlinear p-Laplacian Equation on Exterior Domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.18662 |