Bifurcation in a quasilinear variational problem on a one-dimensional manifold (Q2773596)
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scientific article; zbMATH DE number 1710229
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bifurcation in a quasilinear variational problem on a one-dimensional manifold |
scientific article; zbMATH DE number 1710229 |
Statements
24 February 2002
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quasilinear variation problem
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bifurcation problem
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semilinear differential equation on a manifold
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Ljusternik-Shnirel'man theorem
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Bifurcation in a quasilinear variational problem on a one-dimensional manifold (English)
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The author studies a variational problem for a fourth-order semilinear differential equation defined on the boundary \(\Gamma = \partial\Omega\) of a bounded domain \(\Omega\subset\mathbb R^2\). Problems of such a type arise in elasticity theory. Attention is focused on the bifurcation phenomenon under the study of critical points for a functional constructed. As a result, the author obtains necessary and sufficient conditions for bifurcation in the problem under consideration. The proof is based on a version of the Lyusternik-Shnirel'man theorem.NEWLINENEWLINENEWLINEThe author concludes that the results obtained can be extended to the case of \(\Omega\subset\mathbb R^m\).
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