Branching from degenerate solutions of a nonlinear eigenvalue problem (Q1103853)
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scientific article; zbMATH DE number 4054402
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Branching from degenerate solutions of a nonlinear eigenvalue problem |
scientific article; zbMATH DE number 4054402 |
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Branching from degenerate solutions of a nonlinear eigenvalue problem (English)
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1987
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The author discusses turning points of the solution branch of \(\Delta u+\lambda f(u)=0\) under Robin boundary conditions by Lyapunov-Schmidt type methods. Note that the very last case considered (where \(u^*=0)\) is in error. Generically, there are 1 or 3 arcs of non-trivial solutions. A more detailed study of this last case can be found in \textit{E. N. Dancer} [Proc. London Math. Soc. 23, 699--734 (1971; Zbl 0227.47050)] or \textit{J. B. McLeod} and \textit{D. H. Sattinger} [J. Funct. Anal. 14, 62--84 (1973; Zbl 0275.47045)].
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bifurcation points
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nonlinear elliptic equations
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turning points of the solution branch
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Robin boundary conditions
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Lyapunov-Schmidt type methods
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