Global existence and uniqueness of continuous solution of Urysohn-Volterra equation (Q2714184)
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scientific article; zbMATH DE number 1603989
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global existence and uniqueness of continuous solution of Urysohn-Volterra equation |
scientific article; zbMATH DE number 1603989 |
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12 June 2001
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continuous solutions
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hysteresis operator
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Urysohn-Volterra equation
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system of nonlinear integral equations
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existence
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uniqueness
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Global existence and uniqueness of continuous solution of Urysohn-Volterra equation (English)
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The author considers a system of nonlinear integral equations containing a hysteresis operator \(\mathcal{W}\) NEWLINE\[NEWLINE y(t)=g(t)+\int_{0}^{t}f(t,s,y(s),\mathcal{W}[S[y]](s)) ds,\quad 0\leq t\leq T, NEWLINE\]NEWLINE where \(S[y](t)=h(y(t)).\) The existence and uniqueness of the solution is proved using a more general theorem (based on the Banach fixed point theorem) concerning Volterra operators which, besides being locally Lipschitz continuous, are also bounded.
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