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Solvability of convolution type integro-differential equations on ℝ

  • Integro-Differential Equations
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Abstract

The paper looks for the solutions of integro-differential equations of the form

$$ - \frac{{d\varphi }}{{dx}} + A\varphi (x) = g(x) + B\int_\mathbb{R} {k(x - t)\lambda (t)\varphi (t)dt, x \in \mathbb{R}} $$

in the class of functions which are absolutely continuous and of slow growth on ℝ. It is assumed that A and B are nonnegative parameters, 0 ≤ g ∈ L 1 (ℝ), 0 ≤ k ∈ L 1 (ℝ), ∫ℝ k(x) dx = 1 and 0 ≤ λ(x) ≤ 1 is a measurable function in ℝ. The equation is solved by a special factorization of the corresponding integro-differential operator in combination with appropriately modified standard methods of the theory of convolution type integral equations.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Armenia, Armenia

    Khachatur A. Khachatryan

  2. Faculty of Applied Mathematics and Informatics, Yerevan State University, Armenia

    Emilya A. Khachatryan

Authors
  1. Khachatur A. Khachatryan
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  2. Emilya A. Khachatryan
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Additional information

Original Russian Text © Kh. A. Khachatryan, E. A. Khachatryan, 2007, published in Izvestiya NAN Armenii. Matematika, 2007, No. 3, pp. 65–84.

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Khachatryan, K.A., Khachatryan, E.A. Solvability of convolution type integro-differential equations on ℝ. J. Contemp. Mathemat. Anal. 42, 161–175 (2007). https://doi.org/10.3103/S1068362307030065

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  • DOI: https://doi.org/10.3103/S1068362307030065

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