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Nonlinear boundary-value problems for degenerate differential-algebraic systems

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Abstract

The necessary and sufficient conditions of solvability of nonlinear differential-algebraic boundary-value problems and a convergent iterative scheme of construction of approximations to their solutions are found. An improved classification of the solutions of such problems is given.

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References

  1. A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, De Gruyter,Berlin, 2016.

    Book  Google Scholar 

  2. A. A. Boichuk and L. M. Shegda, “Degenerate nonlinear boundary-value problems,” Ukr. Mat. Zh., 61(9), 1174–1188 (2009).

    Article  MathSciNet  Google Scholar 

  3. S. L. Campbell, Singular Systems of Differential Equations, Pitman, San Francisco, 1980.

    MATH  Google Scholar 

  4. Yu. E. Boyarintsev and V. F. Chistyakov, Algebraic-Differential Systems. Methods of Solution and Studies [in Russian], Nauka, Novosibirsk, 1998.

    Google Scholar 

  5. A. M. Samoilenko, M. I. Shkil’, and V. P. Yakovets’, Linear Systems of Differential Equations with Degeneration [in Ukrainian], Vyshcha Shkola, Kyiv, 2000.

  6. S. M. Chuiko, “On a reduction of the order in a differential-algebraic system,” J. Math. Sci., 235, 2–14 (2018).

    Article  MathSciNet  Google Scholar 

  7. S. M. Chuiko and O. V. Nesmelova, “On the transformation of a nonlinear Noetherian differential-algebraic boundary-value problem to a noncritical case,” Visn. Khark. Nats. Univ. im. V.N. Karazina. Ser. Mat., Prikl. Mat., Mekh., 90, 60–72 (2019).

    MATH  Google Scholar 

  8. S. M. Chuiko, “The generalized Green operator of a linear Noetherian differential-algebraic boundary-value problem,” Matem. Trudy, 23(1), 1–20 (2020).

    Google Scholar 

  9. M. A. Perepelitsa and A. A. Pokutnyi, “Study of the solvability of weakly nonlinear differential-algebraic systems,” Vestn. YuUGU. Ser. Mat. Model. Progr., 6(4), 55–62 (2013).

    MATH  Google Scholar 

  10. S. M. Chuiko, “Domain of convergence of an iterative procedure for an autonomous boundary value problem,” Nonlin. Oscill., 9(3), 405–422 (2006).

    Article  MathSciNet  Google Scholar 

  11. A. A. Boichuk and S. A. Krivosheya, “A critical periodic boundary value problem for a matrix Riccati equation,” Differ. Equ., 37(4), 464–471 (2001).

    Article  MathSciNet  Google Scholar 

  12. S. M. Chuiko, “Nonlinear matrix differential-algebraic boundary value problem,” Lobachevskii J. Math., 38(2), 236–244 (2017).

    Article  MathSciNet  Google Scholar 

  13. V. Gutlyanskii, O. Nesmelova, and V. Ryazanov, “On a model semilinear elliptic equation in the plane,” J. Math. Sci., 220(5), 603–614 (2017).

    Article  MathSciNet  Google Scholar 

  14. I. I. Skrypnik, “Removability of isolated singularities for anisotropic elliptic equations with gradient absorption,” Israel J. Math., 215(1), 163–179 (2016).

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Donbas State Pedagogical University, Slov’yans’k, Ukraine

    Sergii Mykhailovych Chuiko

  2. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slov’yans’k, Ukraine

    Ol’ga Volodymyrivna Nesmelova

Authors
  1. Sergii Mykhailovych Chuiko
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  2. Ol’ga Volodymyrivna Nesmelova
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Corresponding author

Correspondence to Sergii Mykhailovych Chuiko.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 3, pp. 313–324 July–September, 2020.

The work was financially supported by the Ministry of Education and Science of Ukraine, project No. 0118U003390.

Translated from Ukrainian by V.V. Kukhtin

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Chuiko, S.M., Nesmelova, O.V. Nonlinear boundary-value problems for degenerate differential-algebraic systems. J Math Sci 252, 463–471 (2021). https://doi.org/10.1007/s10958-020-05174-5

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  • DOI: https://doi.org/10.1007/s10958-020-05174-5

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