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On Solvability of One Class of Nonlinear Integral Equations on Whole Line with Two Monotone Nonlinearities

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Abstract

We investigate a class of nonlinear singular integral equations with two monotone nonlinearities on the whole line. These equations have both theoretical and practical interest. We prove the existence theorem of a solution and the uniqueness theorem in a certain class of continuous and odd on \(\mathbb {R}\setminus\{0\}\) functions. The results of the work summarize some previously obtained research results in this direction. We find the limits of the solution of the equation at \(\pm\infty\). For obtained solution we investigate some its properties. We also establish the integral asymptotic for the constructed solutions. The results are illustrated by examples of the equations under consideration.

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Funding

This work is supported by the Russian Science Foundation under grant No 19-11-00223 and per-formed at Moscow State University. We thank the referee for useful remarks.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Kh. A. Khachatryan

  2. Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, Armenia

    Kh. A. Khachatryan

  3. Armenian National Agrarian University, Yerevan, Armenia

    S. M. Andriyan

Authors
  1. Kh. A. Khachatryan
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  2. S. M. Andriyan
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Correspondence to Kh. A. Khachatryan.

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Khachatryan, K.A., Andriyan, S.M. On Solvability of One Class of Nonlinear Integral Equations on Whole Line with Two Monotone Nonlinearities. P-Adic Num Ultrametr Anal Appl 12, 259–275 (2020). https://doi.org/10.1134/S2070046620040019

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  • DOI: https://doi.org/10.1134/S2070046620040019

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