A note on bifurcations of \(u^{\prime\prime}+\mu (u-u^k)=0\) \((4 \leq k\in \mathbb{Z}^+)\) (Q1574987)
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scientific article; zbMATH DE number 1490815
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on bifurcations of \(u^{\prime\prime}+\mu (u-u^k)=0\) \((4 \leq k\in \mathbb{Z}^+)\) |
scientific article; zbMATH DE number 1490815 |
Statements
A note on bifurcations of \(u^{\prime\prime}+\mu (u-u^k)=0\) \((4 \leq k\in \mathbb{Z}^+)\) (English)
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22 March 2002
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Consider the boundary value problem \((*)\) \(u'' + \mu (u-u^k)=0\), \(u(0)=u(\pi)=0\), where \(\mu\) is a real parameter, \(4 \leq k \in \mathbb{Z}^+\). The author applies the Lyapunov-Schmidt method to \((*)\) and studies the corresponding bifurcation equation.
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boundary value problem
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Lyapunov-Schmidt method
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singularly theory
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bifurcation
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0.97849905
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0.8525506
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0.8311234
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0.83091146
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0.83079815
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0.8303957
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0.8290901
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0.8290158
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