We consider a class of nonlinear convolution type integral equations with a noncompact Hammerstein operator on the half-line and on the whole line. Under certain conditions on nonlinearity, we prove the existence of a one-parameter family of positive solutions and study the asymptotic behavior of the solutions at infinity. The results are illustrated by examples of the equations under consideration.
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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 17, No. 1, 2017, pp. 91-108.
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Khachatryan, K.A., Petrosyan, H.S. One-Parameter Families of Positive Solutions of Some Classes of Nonlinear Convolution Type Integral Equations. J Math Sci 231, 153–167 (2018). https://doi.org/10.1007/s10958-018-3812-2
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DOI: https://doi.org/10.1007/s10958-018-3812-2