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On the solvability of a nonlinear second-order integro-differential equation with sum-difference kernel on a semiaxis

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Abstract

We consider a class of nonlinear second-order integro-differential equations with sum-difference kernel on a positive semiaxis. By constructing a special factorization of the initial linear integro-differential operator, we prove the existence of a nonnegative, nontrivial, and monotonically increasing solution and determine its asymptotic behavior at infinity. The relevant examples are presented.

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Authors and Affiliations

  1. Institute of Mathematics of the NAN of RA, 24b, Bagramyan Prosp., Erevan, 0019, Republic of Armenia

    Khachatur A. Khachatryan

  2. Armenian State Agrarian University, 74, Teryan Str., Erevan, 0009, Republic of Armenia

    Mikael G. Kostanyan

Authors
  1. Khachatur A. Khachatryan
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  2. Mikael G. Kostanyan
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Correspondence to Khachatur A. Khachatryan.

Additional information

Translated from Russian by V. V. Kukhtin

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 8, No. 3, pp. 404–420, July–August, 2011.

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Khachatryan, K.A., Kostanyan, M.G. On the solvability of a nonlinear second-order integro-differential equation with sum-difference kernel on a semiaxis. J Math Sci 181, 65–77 (2012). https://doi.org/10.1007/s10958-012-0676-8

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  • DOI: https://doi.org/10.1007/s10958-012-0676-8

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