Topological transversality. II: Applications to the Neumann problem for \(y''=f(t,y,y')\) (Q790318)
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scientific article; zbMATH DE number 3847778
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Topological transversality. II: Applications to the Neumann problem for \(y''=f(t,y,y')\) |
scientific article; zbMATH DE number 3847778 |
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Topological transversality. II: Applications to the Neumann problem for \(y''=f(t,y,y')\) (English)
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1983
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[For part I see ibid. 89, 53-67 (1980; Zbl 0453.34018).] In this paper the Neumann problem for the nonlinear equation \(y''=f(t,y,y')\) is studied. A priori bounds are derived and the results of Granas, Guenther and Lee, are invoked to obtain existence theorems. The existence theorems are in many cases quite different from those of the Dirichlet problem, e.g. it is possible to obtain general existence theorems where f(t,y,y') can grow very rapidly in the y' variable.
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Neumann problem
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A priori bounds
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Dirichlet problem
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