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On the Volterra integral equation with weakly singular kernel. (English) Zbl 1110.45003

Summary: We give sufficient conditions for the existence of at least one integrable solution of equation \(x(t)=f(t)+\int _{0}^{t} K(t,s)g(s,x(s))\,ds\). Our assumptions and proofs are expressed in terms of measures of noncompactness.

MSC:

45G05 Singular nonlinear integral equations
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