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Of the functional-integral equation of Volterra type with weakly singular kernel. (English) Zbl 1274.45005

Summary: We give sufficient conditions for the existence of \(L^p\)-solution of a Volterra functional-integral equation in a Banach space. Our assumptions and proofs are expressed in terms of measures of noncompactness.

MSC:

45G05 Singular nonlinear integral equations
45D05 Volterra integral equations
45N05 Abstract integral equations, integral equations in abstract spaces
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
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