Fundamental properties and asymptotic shapes of the singular and classical radial solutions for supercritical semilinear elliptic equations
Nonlinear Differential Equations and Applications Volume 27
Page 52-
published_at 2020-10-10
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| File | |
| Title ( eng ) |
Fundamental properties and asymptotic shapes of the singular and classical radial solutions for supercritical semilinear elliptic equations
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| Creator |
Miyamoto Yasuhito
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| Source Title |
Nonlinear Differential Equations and Applications
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| Volume | 27 |
| Start Page | 52 |
| Abstract |
We study singular radial solutions of the semilinear elliptic equation Δu+f(u)=0 on finite balls in RN with N≥3. We assume that f satisfies either f(u)=up+o(up) with p>(N+2)/(N−2) or f(u)=eu+o(eu) as u→∞. We provide the existence and uniqueness of the singular radial solution, and show the convergence of regular radial solutions to the singular solution. Some applications to the bifurcation diagram of an elliptic Dirichlet problem are also given. Our results generalize and improve some known results in the literature.
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| Keywords |
Semilinear elliptic equation
Singular solution
Supercritical
Uniqueness
Existence
Asymptotic shape
MSC: 35J61
MSC: 35A05
MSC: 35A24
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| Descriptions |
The first author was supported by JSPS KAKENHI Grant Number JP16K05225 and the second author was supported by JSPS KAKENHI Grant Number 17K05333. This work was also supported by Research Institute for Mathematical Sciences, a Joint Usage/Research Center located in Kyoto University.
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
Springer
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| Date of Issued | 2020-10-10 |
| Rights |
This is not the published version. Please cite only the published version. この論文は出版社版ではありません。引用の際には出版社版をご確認、ご利用ください。
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| Publish Type | Author’s Original |
| Access Rights | open access |
| Source Identifier |
[ISSN] 1021-9722
[ISSN] 1420-9004
[DOI] 10.1007/s00030-020-00658-4
[DOI] https://doi.org/10.1007/s00030-020-00658-4
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