We investigate qualitative properties of solutions of special classes of convolution type nonlinear integral equations on the whole line. We study the asymptotic properties, continuity, and monotonicity of arbitrary nontrivial bounded solutions. Depending on the properties of the kernel of the equation, we find out whether there exist nontrivial bounded solutions with a finite limit at ±∞. Based on the obtained results, we establish uniqueness theorems for large classes of bounded functions. The results obtained are illustrated by examples from applications.
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Translated from Problemy Matematicheskogo Analiza 110, 2021, pp. 105-117.
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Khachatryan, K.A., Petrosyan, H.S. Integral Equations on the Whole Line with Monotone Nonlinearity and Difference Kernel. J Math Sci 255, 790–804 (2021). https://doi.org/10.1007/s10958-021-05416-0
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DOI: https://doi.org/10.1007/s10958-021-05416-0