Existence of two infinite families of solutions to a singular superlinear equation on exterior domains
We are concerned with the radial solutions of the Dirichlet problem $-\Delta u=K(|x|)f(u)$ on the exterior of the ball of radius $R>0$ centered at the origin in $\mathbb{R}^N \text{ with } N\geq 3$ where $f$ is superlinear at $\infty$ and has a singularity at $0$ with $f(u) \sim \frac{1}{|u|^{q-1...
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University of Szeged
2024-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11122 |
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| author | Narayan Aryal Joseph Iaia |
| author_facet | Narayan Aryal Joseph Iaia |
| author_sort | Narayan Aryal |
| collection | DOAJ |
| description | We are concerned with the radial solutions of the Dirichlet problem $-\Delta u=K(|x|)f(u)$ on the exterior of the ball of radius $R>0$ centered at the origin in $\mathbb{R}^N \text{ with } N\geq 3$ where $f$ is superlinear at $\infty$ and has a singularity at $0$ with $f(u) \sim \frac{1}{|u|^{q-1}u} \text{ and } 0<q<1$ for small $u$. We prove that if $K(|x|)\sim |x|^{-\alpha}$ with $\alpha>2(N-1)$ then there exist two infinite families of sign-changing radial solutions. |
| format | Article |
| id | doaj-art-ff930af605514adaad83049be9829c01 |
| institution | DOAJ |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-ff930af605514adaad83049be9829c012025-08-20T02:42:30ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-11-0120246811410.14232/ejqtde.2024.1.6811122Existence of two infinite families of solutions to a singular superlinear equation on exterior domainsNarayan Aryal0Joseph IaiaUniversity Of North Texas TX, U.S.A.We are concerned with the radial solutions of the Dirichlet problem $-\Delta u=K(|x|)f(u)$ on the exterior of the ball of radius $R>0$ centered at the origin in $\mathbb{R}^N \text{ with } N\geq 3$ where $f$ is superlinear at $\infty$ and has a singularity at $0$ with $f(u) \sim \frac{1}{|u|^{q-1}u} \text{ and } 0<q<1$ for small $u$. We prove that if $K(|x|)\sim |x|^{-\alpha}$ with $\alpha>2(N-1)$ then there exist two infinite families of sign-changing radial solutions.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11122exterior domainssingularsuperlinearradial solution |
| spellingShingle | Narayan Aryal Joseph Iaia Existence of two infinite families of solutions to a singular superlinear equation on exterior domains Electronic Journal of Qualitative Theory of Differential Equations exterior domains singular superlinear radial solution |
| title | Existence of two infinite families of solutions to a singular superlinear equation on exterior domains |
| title_full | Existence of two infinite families of solutions to a singular superlinear equation on exterior domains |
| title_fullStr | Existence of two infinite families of solutions to a singular superlinear equation on exterior domains |
| title_full_unstemmed | Existence of two infinite families of solutions to a singular superlinear equation on exterior domains |
| title_short | Existence of two infinite families of solutions to a singular superlinear equation on exterior domains |
| title_sort | existence of two infinite families of solutions to a singular superlinear equation on exterior domains |
| topic | exterior domains singular superlinear radial solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11122 |
| work_keys_str_mv | AT narayanaryal existenceoftwoinfinitefamiliesofsolutionstoasingularsuperlinearequationonexteriordomains AT josephiaia existenceoftwoinfinitefamiliesofsolutionstoasingularsuperlinearequationonexteriordomains |