A bifurcation theorem for potential operators with infinite dimensional kernel (Q1900359)
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scientific article; zbMATH DE number 811175
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A bifurcation theorem for potential operators with infinite dimensional kernel |
scientific article; zbMATH DE number 811175 |
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A bifurcation theorem for potential operators with infinite dimensional kernel (English)
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31 October 1995
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Let \(X\) be a Hilbert space and \(f: X\to \mathbb{R}\) a smooth function with \(f'(0)= 0\). The authors study the equation \(f'(x)= \lambda x\) under the assumption that \(f'\) satisfies a Palais-Smale condition. They show, in particular, that every isolated eigenvalue of \(f''(0)\) is a bifurcation point.
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smooth function
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Palais-Smale condition
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bifurcation point
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0.809768557548523
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0.8074244856834412
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