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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2507.17863 |
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| _version_ | 1866908463736553472 |
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| author | Ahamed, Md Suzan Iaia, Joseph |
| author_facet | Ahamed, Md Suzan Iaia, Joseph |
| contents | In this paper, we study radial solutions of $Δu + K(|x|) f(u)+\frac{ (N-2)^2 u}{|x|^{2+(N-2)δ}} =0, \ 0<δ<2$ in the exterior of the ball of radius $R>0$ in ${\mathbb R}^{N}$ where $f$ grows superlinearly at infinity and is singular at $0$ with $f(u) \sim -\frac{1}{|u|^{q-1}u}$ and $0<q<1$ for small $u$. We assume $K(|x|) \sim |x|^{-α}$ for large $|x|$ and establish the existence of an infinite number of sign-changing solutions when $N+q(N-2) <α<2(N-1).$ We also prove nonexistence for $0<α\leq2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and nonexistence of sign-changing solutions for linearly perturbed superlinear equations on exterior domains Ahamed, Md Suzan Iaia, Joseph Analysis of PDEs In this paper, we study radial solutions of $Δu + K(|x|) f(u)+\frac{ (N-2)^2 u}{|x|^{2+(N-2)δ}} =0, \ 0<δ<2$ in the exterior of the ball of radius $R>0$ in ${\mathbb R}^{N}$ where $f$ grows superlinearly at infinity and is singular at $0$ with $f(u) \sim -\frac{1}{|u|^{q-1}u}$ and $0<q<1$ for small $u$. We assume $K(|x|) \sim |x|^{-α}$ for large $|x|$ and establish the existence of an infinite number of sign-changing solutions when $N+q(N-2) <α<2(N-1).$ We also prove nonexistence for $0<α\leq2$. |
| title | Existence and nonexistence of sign-changing solutions for linearly perturbed superlinear equations on exterior domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.17863 |