Peano's theorem for implicit differential equations (Q5940335)
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scientific article; zbMATH DE number 1624819
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Peano's theorem for implicit differential equations |
scientific article; zbMATH DE number 1624819 |
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Peano's theorem for implicit differential equations (English)
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22 March 2002
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Peano's theorem
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implicit differential equations
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lower and upper solutions
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The author proves an existence result for the Cauchy problem NEWLINE\[NEWLINEF(t,x,x', \ldots,x^{(m)})=0,\quad x(0)=x_0,x'(0)=x_1, \ldots, x^{(m-1)}(0)=x_{m-1},NEWLINE\]NEWLINE with \(m \in {\mathbb N}\). He looks for solutions in the Lipschitz sense and gives an example where there exist no classical solutions. In the proofs, the viscosity lower and upper solutions method is used.
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