Solvability of an infinite system of integral equations on the real half-axis (Q780539)
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scientific article; zbMATH DE number 7221205
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solvability of an infinite system of integral equations on the real half-axis |
scientific article; zbMATH DE number 7221205 |
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Solvability of an infinite system of integral equations on the real half-axis (English)
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15 July 2020
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In the space \(BC(\mathbb{R}_+, \ell_\infty)\) of all sequences \(x(t)= (x_n(t))_n\), the authors study the solvability of the Hammerstein-Volterra equation \[x_n(t)= a_n(t)+ f_n(t,x(t)) \int^t_0 k_n(t,s)g_n(s,x(s))\,ds.\] To this end, they impose a set of 10 technical conditions on the data \(a= (a_n)_n\), \(f=(f_n)_n\), and \(g= (g_n)_n\) in order to apply a fixed point theorem which builds on a certain measure of noncompactness.
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space of functions continuous and bounded on the half-axis
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sequence space
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measure of noncompactness
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fixed point theorem of Darbo type
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infinite system of integral equations
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