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Solvability of an infinite system of integral equations on the real half-axis. (English) Zbl 1512.47096

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 ten 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.

MSC:

47N20 Applications of operator theory to differential and integral equations
45G15 Systems of nonlinear integral equations
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
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