On \(x'=f(t,x)\) and Henstock-Kurzweil integrals (Q810222)
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scientific article; zbMATH DE number 4212471
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(x'=f(t,x)\) and Henstock-Kurzweil integrals |
scientific article; zbMATH DE number 4212471 |
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On \(x'=f(t,x)\) and Henstock-Kurzweil integrals (English)
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1991
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The authors take into consideration the Cauchy problem \(x'=f(t,x),\quad x(\tau)=\xi,\) in Henstock-Kurzweil integral setting. More precisely, they prove an existence result which extends the Carathéodory theorem and a continuous dependence result with respect to a parameter. Examples are given to illustrate these results.
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Cauchy problem
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Henstock-Kurzweil integral
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existence
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continuous dependence
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