We consider weakly nonlinear Fredholm integral equations with degenerate kernel in Banach spaces and establish a necessary condition and sufficient conditions for the existence of solutions of equations of this kind. The convergent iterative procedures are proposed for the construction either of a single solution or of at least one possible solution.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 11, pp. 1477–1490, November, 2015.
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Zhuravl’ov, V.F. Weakly Nonlinear Fredholm Integral Equations with Degenerate Kernel in Banach Spaces. Ukr Math J 67, 1662–1677 (2016). https://doi.org/10.1007/s11253-016-1181-x
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DOI: https://doi.org/10.1007/s11253-016-1181-x