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Least-squares method in the theory of ill-posed linear boundary-value problems with pulse action

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Ukrainian Mathematical Journal Aims and scope

We use the scheme of the classic least-squares method for the construction of an approximate pseudosolution of a linear ill-posed boundary-value problem with pulse action for a system of ordinary differential equations in the critical case. The pseudosolution obtained is represented in the form of partial sums of a generalized Fourier series.

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References

  1. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

  2. A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, VSP, Utrecht (2004).

    MATH  Google Scholar 

  3. Š. Schwabik, “Differential equations with interface conditions,” Čas. Pěstov. Mat., 105, 391–408 (1980).

    MATH  MathSciNet  Google Scholar 

  4. A. A. Boichuk and S. M. Chuiko, “Generalized Green operator for an impulsive boundary-value problem with switchings,” Nelin. Kolyvannya, 10, No. 1, 51–65 (2007).

    MathSciNet  Google Scholar 

  5. S. M. Chuiko, “Green operator of a boundary-value problem with pulse action,” Differents. Uravn., 37, No. 8, 1132–1135 (2001).

    MathSciNet  Google Scholar 

  6. A. N. Tikhonov, “On the solution of ill-posed problems and the method of regularization,” Dokl. Akad. Nauk SSSR, 151, No. 3, 501–504 (1963).

    MathSciNet  Google Scholar 

  7. N. M. Krylov, Selected Works [in Russian], Vol. 1, Academy of Sciences of Ukrainian SSR, Kiev (1961).

    Google Scholar 

  8. N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  9. S. M. Chuiko, “Least-squares method in the theory of ill-posed boundary-value problems,” Visn. Shevchenko Kyiv. Nats. Univ., No. 7, 51–53 (2007).

    Google Scholar 

  10. L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).

    Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 5, pp. 690–697, May, 2010.

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Chuiko, S.M. Least-squares method in the theory of ill-posed linear boundary-value problems with pulse action. Ukr Math J 62, 794–803 (2010). https://doi.org/10.1007/s11253-010-0389-4

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  • DOI: https://doi.org/10.1007/s11253-010-0389-4

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