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On the Solvability of a Class of Nonlinear Hammerstein—Stieltjes Integral Equations on the Whole Line

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Abstract

We consider a nonlinear integral equation on the whole line with a Hammerstein-Stieltjes integral operator whose pre-kernel is a continuous distribution function. Under certain conditions imposed on the nonlinearity, we prove constructive existence and uniqueness theorems for nonnegative monotone bounded solutions. Some qualitative properties of the constructed solution are also studied. In particular, the results proved in the paper contain a theorem of O. Diekmann as a special case.

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Funding

This work is supported by the Russian Science Foundation under grant 19-11-00223 and performed at Moscow State University.

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Correspondence to Kh. A. Khachatryan or H. S. Petrosyan.

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Russian Text © The Author(s), 2020, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Vol. 308, pp. 253–264.

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Khachatryan, K.A., Petrosyan, H.S. On the Solvability of a Class of Nonlinear Hammerstein—Stieltjes Integral Equations on the Whole Line. Proc. Steklov Inst. Math. 308, 238–249 (2020). https://doi.org/10.1134/S0081543820010198

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  • DOI: https://doi.org/10.1134/S0081543820010198

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