An existence theorem for a functional-integral equation with deviating arguments (Q690394)
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scientific article; zbMATH DE number 459010
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An existence theorem for a functional-integral equation with deviating arguments |
scientific article; zbMATH DE number 459010 |
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An existence theorem for a functional-integral equation with deviating arguments (English)
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17 April 1994
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Using the conjunction of the techniques associated with the measure of weak noncompactness and the Schauder fixed point theorem the authors prove an existence result for a functional-integral equation of the form \[ x(t) = f(t,r\int^ 1_ 0 k(t,s)g(s,x(h_ 1(s)),x(h_ 2(s)),\dots,x(h_ n(s)))ds), \] where \(t\in [0,1]\) and \(x = x(t)\) is the unknown function belonging to the space \(L^ 1[0,1]\).
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deviating arguments
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measure of weak noncompactness
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Schauder fixed point theorem
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existence
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functional-integral equation
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