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Solution of Volterra operator-integral equations in the nonregular case by the successive approximation method

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Abstract

The branches of solutions of a nonlinear integral equation of Volterra type in a Banach space are constructed by the successive approximation method. We consider the case in which a solution may have an algebraic branching point. We reduce the equation to a system regular in a neighborhood of the branching point. Continuous and generalized solutions are considered. General existence theorems are used to study an initial-boundary value problem with degeneration in the leading part.

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Authors and Affiliations

  1. Irkutsk State University, Irkutsk, Russia

    N. A. Sidorov, D. N. Sidorov & A. V. Krasnik

  2. Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia

    N. A. Sidorov, D. N. Sidorov & A. V. Krasnik

  3. Institute of Power Engineering Systems, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia

    N. A. Sidorov, D. N. Sidorov & A. V. Krasnik

Authors
  1. N. A. Sidorov
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  2. D. N. Sidorov
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  3. A. V. Krasnik
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Original Russian Text © N.A. Sidorov, D.N. Sidorov, A.V. Krasnik, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 6, pp. 874–882.

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Sidorov, N.A., Sidorov, D.N. & Krasnik, A.V. Solution of Volterra operator-integral equations in the nonregular case by the successive approximation method. Diff Equat 46, 882–891 (2010). https://doi.org/10.1134/S001226611006011X

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  • DOI: https://doi.org/10.1134/S001226611006011X

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