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Boundary-Value Problems for the Evolutionary Schrödinger Equation. II

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We prove a series of results on the existence of solutions of boundary-value problems for the Schrödinger equation in the resonance (critical) case. Iterative procedures are proposed for the construction of solutions of the corresponding problems in the nonlinear case.

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References

  1. M. Reed and B. Simon, Methods of Modern Mathematical Physics. Harmonic Analysis. Self-Adjointness [in Russian], Vol. 2, Mir, Moscow (1978).

    Google Scholar 

  2. A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, De Gruyter, Berlin; Boston (2016).

  3. A. Samoilenko and R. Petrishin, Multifrequency Oscillations of Nonlinear Systems, Springer, Dordrecht (2004).

    MATH  Google Scholar 

  4. S. G. Krein, Linear Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  5. A. A. Boichuk and A. A. Pokutnyi, “Theory of bifurcations of the Schrödinger equation,” Different. Equat., 53, No. 7, 882–890 (2017).

    MATH  Google Scholar 

  6. O. O. Pokutnyi, “Generalized-inverse operator in the Fréchet, Banach and Hilbert spaces,” Bull. Kiev Univ. Ser. Phys. Math., No. 4, 158–161 (2013).

    MATH  Google Scholar 

  7. A. Robertson and V. Robertson, Topological Vector Spaces [in Russian], Mir, Moscow (1967).

    MATH  Google Scholar 

  8. M. F. Atiyah, K-Theory: Lectures, Notes by D. W. Anderson, fall, 1964, Benjamin Inc., New-York, Amsterdam (1967).

  9. D. A. Klyushin, S. I. Lyashko, D. A. Nomirovskii, Yu. I. Petunin, and V. V. Semenov, Generalized Solutions of Operator Equations and Extreme Elements, Springer Science+Business Media, New York–Dordrecht–Heidelberg–London (2012).

  10. B. A. Biletskyi, A. A. Boichuk, and A. A. Pokutnyi, “Periodic problems of difference equations and ergodic theory,” in: Abstr. Appl. Anal., Article ID 928587 (2011); http://www.hindawi.com/journals/aaa/2011/928587.

  11. A. A. Pokutnyi, “Periodic solutions of the Hill equation,” J. Math. Sci., 197, No. 1, 114–121 (2014).

    Article  MathSciNet  Google Scholar 

  12. A. A. Pokutnyi, “Representation of the solutions of boundary-value problems for the Schrödinger equation in a Hilbert space,” J. Math. Sci., 205, No. 6, 821–831 (2015).

    Article  MathSciNet  Google Scholar 

  13. A. A. Boichuk and A. A. Pokutnyi, “Solutions of the Schrödinger equation in a Hilbert space,” Bound. Value Probl., 2014, No. 4 (2014); http://www.boundaryvalueproblems.com/content/2014/1/4.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivs’ka Str., 3, Kyiv, 01024, Ukraine

    D. Bihun & O. O. Pokutnyi

Authors
  1. D. Bihun
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  2. O. O. Pokutnyi
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Correspondence to O. O. Pokutnyi.

Additional information

Published in Neliniini Kolyvannya, Vol. 22, No. 4, pp. 439–457, October–December, 2019.

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Bihun, D., Pokutnyi, O.O. Boundary-Value Problems for the Evolutionary Schrödinger Equation. II. J Math Sci 254, 179–200 (2021). https://doi.org/10.1007/s10958-021-05297-3

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  • DOI: https://doi.org/10.1007/s10958-021-05297-3

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