We investigate one class of Urysohn-type nonlinear integral equations with noncompact operator. It is assumed that a Wiener–Hopf–Hankel-type linear integral operator is a local minorant for the initial Urysohn operator. We prove an alternative theorem on the existence of positive solutions and investigate the asymptotic behavior of the obtained solutions at infinity.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 1, pp. 110–118, January, 2011.
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Khachatryan, A.K., Khachatryan, K.A. On the construction of a nonnegative solution for one class of Urysohn-type nonlinear integral equations on a semiaxis. Ukr Math J 63, 134–145 (2011). https://doi.org/10.1007/s11253-011-0492-1
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DOI: https://doi.org/10.1007/s11253-011-0492-1