Continuity moduli criteria for ODE's in a Banach space (Q788181)
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scientific article; zbMATH DE number 3842315
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuity moduli criteria for ODE's in a Banach space |
scientific article; zbMATH DE number 3842315 |
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Continuity moduli criteria for ODE's in a Banach space (English)
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1982
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The main result of this paper is a modulus of continuity criterion for the convergence of successive approximations to the solution of the Cauchy problem \(x'(t)=f(t,x(t))\), 0\(\leq t\leq T\), \(x(0)=z\) in infinite- dimensional Banach spaces. This new criterion seems to contain all previously known criteria of its type. Many examples and related results are also presented.
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modulus of continuity criterion
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Cauchy problem
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infinite-dimensional Banach spaces
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