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Method for solving a nonlinear spectral problem for a system of ordinary differential equations with redundant conditions

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Abstract

We consider a nonlinear spectral problem for a system of ordinary differential equations supplemented with nonlocal conditions given by a Stieltjes integral. In addition to the main conditions, the solution is subjected to redundant conditions, which are nonlocal as well. To ensure the nontrivial solvability of the “overdetermined” problem thus obtained, the original problem is replaced by an auxiliary problem, which is consistent under the whole set of conditions. We obtain this auxiliary problem from the original one by allowing a discrepancy of a certain form. We study the resulting problem and provide a numerical solution method.

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Authors and Affiliations

  1. Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia

    A. A. Abramov & L. F. Yukhno

  2. Moscow Institute of Physics and Technology, Moscow, Russia

    A. A. Abramov & L. F. Yukhno

  3. Institute for Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    A. A. Abramov & L. F. Yukhno

  4. National Research Nuclear University MEPHI (Moscow Engineering Physics Institute), Moscow, Russia

    A. A. Abramov & L. F. Yukhno

Authors
  1. A. A. Abramov
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  2. L. F. Yukhno
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Correspondence to A. A. Abramov.

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Original Russian Text © A.A. Abramov, L.F. Yukhno, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 7, pp. 866–875.

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Abramov, A.A., Yukhno, L.F. Method for solving a nonlinear spectral problem for a system of ordinary differential equations with redundant conditions. Diff Equat 51, 862–871 (2015). https://doi.org/10.1134/S0012266115070058

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  • DOI: https://doi.org/10.1134/S0012266115070058

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