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On solvability of one class of integral equations on whole line with monotonic and convex nonlinearity

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Abstract

The paper studies the issues of existence, absence and uniqueness of nontrivial nonnegative and bounded solution for one class of nonlinear integral equations on the whole line with symmetric and positive kernel. In the class of integral equations under study, the nonlinearity is a monotonic and convex function on the positive part of the real axis. The above mentioned class of integral equations, with various particular representations of the kernel and nonlinearity, has applications in many areas of mathematical physics and mathematical biology. At the end of the work particular examples of kernel and nonlinearity satisfying all conditions of the proved statements are given.

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Funding

The research by Kh.A. Khachatryan and H.S. Petrosyan was supported by the Russian Science Foundation, project no. 19-11-00223.

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Authors and Affiliations

  1. Yerevan State University, Alex Manoogian St., Yerevan, 0025, Armenia

    Kh.A. Khachatryan

  2. Lomonosov Moscow State University, Moscow, 119991, Russia

    Kh.A. Khachatryan & H.S. Petrosyan

  3. Armenian National Agrarian University, 74 Teryan St., Yerevan, 0009, Armenia

    H.S. Petrosyan

  4. Russian-Armenian University, Hovsep Emin 123, Yerevan, 0051, Armenia

    A. R. Hakobyan

Authors
  1. Kh.A. Khachatryan
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  2. H.S. Petrosyan
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  3. A. R. Hakobyan
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Corresponding author

Correspondence to A. R. Hakobyan.

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Khachatryan, K., Petrosyan, H. & Hakobyan, A.R. On solvability of one class of integral equations on whole line with monotonic and convex nonlinearity. J Math Sci 271, 610–624 (2023). https://doi.org/10.1007/s10958-023-06424-y

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  • DOI: https://doi.org/10.1007/s10958-023-06424-y

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