Article
| Title: | Exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems (English) |
| Author: | Huang, Shao-Yuan |
| Author: | Hsieh, Ping-Han |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 1081-1098 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems$$ \begin {cases} -[\phi (u^{\prime })]^{\prime }=\lambda u^{p} \Bigl (1-\dfrac {u}{N} \Bigr ) & \text {in} \^^M( -L,L) , \\ u(-L)=u(L)=0,\end {cases} $$ where $p>1$, $N>0$, $\lambda >0$ is a bifurcation parameter, $L>0$ is an evolution parameter, and $\phi (u)$ is either $\phi (u)=u$ or $\phi (u)=u/\sqrt {1-u^{2}}$. We prove that the corresponding bifurcation curve is $\subset $-shape. Thus, the exact multiplicity of positive solutions can be obtained. (English) |
| Keyword: | positive solution |
| Keyword: | bifurcation curve |
| Keyword: | Minkowski-curvature problem, logistic problem |
| MSC: | 34B15 |
| MSC: | 34B18 |
| MSC: | 34C23 |
| MSC: | 74G35 |
| idZBL: | Zbl 07790562 |
| DOI: | 10.21136/CMJ.2023.0359-22 |
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| Date available: | 2023-11-23T12:21:50Z |
| Last updated: | 2024-12-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151948 |
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