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Ufimsk. Mat. Zh., 2011, Volume 3, Issue 3, Pages 80–92 (Mi ufa104)  

This article is cited in 5 scientific papers (total in 5 papers)

Approximate properties of the root functions generated by the correctly solvable boundary value problems for higher order ordinary differential equations

B. E. Kanguzhin, D. B. Nurakhmetov, N. E. Tokmagambetov

Al-Farabi Kazakh National University, Almaty, Kazakhstan

Abstract: In this work properties of systems of root functions generated by the correctly solvable boundary value problems for higher order ordinary differential equations are studied. The biorthogonal systems of functions corresponding to the system of root functions are constructed. The resulting systems of root functions are minimal systems. The completeness of systems of root functions in $L_2(0,1)$ is proved. The algorithm for the inverse problem is given by reconstruction of the boundary functions. Moreover, some identities are found for the eigenvalues of the considered operator.

Keywords: ordinary differential equations, the system of root functions, the biorthogonal system, the eigenvalues, the completeness of the system of functions, correctly solvable, boundary value problems, inner boundary conditions, nonlocal boundary conditions.

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Bibliographic databases:
UDC: 517.9
Received: 14.07.2011

Citation: B. E. Kanguzhin, D. B. Nurakhmetov, N. E. Tokmagambetov, “Approximate properties of the root functions generated by the correctly solvable boundary value problems for higher order ordinary differential equations”, Ufimsk. Mat. Zh., 3:3 (2011), 80–92

Citation in format AMSBIB
\Bibitem{KanNurTok11}
\by B.~E.~Kanguzhin, D.~B.~Nurakhmetov, N.~E.~Tokmagambetov
\paper Approximate properties of the root functions generated by the correctly solvable boundary value problems for higher order ordinary differential equations
\jour Ufimsk. Mat. Zh.
\yr 2011
\vol 3
\issue 3
\pages 80--92
\mathnet{http://mi.mathnet.ru/ufa104}
\zmath{https://zbmath.org/?q=an:1249.47026}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. E. Kanguzhin, D. B. Nurakhmetov, N. E. Tokmagambetov, “Laplace operator with $\delta$-like potentials”, Russian Math. (Iz. VUZ), 58:2 (2014), 6–12  mathnet  crossref
    2. Kanguzhin B.E., Tokmagambetov N.E., “A Regularized Trace Formula For a Well-Perturbed Laplace Operator”, Dokl. Math., 91:1 (2015), 1–4  crossref  mathscinet  zmath  isi  scopus
    3. A. A. Sarsenbi, L. K. Zhumanova, “First Regularized Trace of Integro-Differential Sturm-Liouville Operator on a Segment With Punctured Points At Generalized Conditions of Bonding in Deleted Points”, Applications of Mathematics in Engineering and Economics, AMEE'16, AIP Conference Proceedings, 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Physics, 2016, UNSP 040009  crossref  isi  scopus
    4. A. Sh. Aimakhanova, S. Kh. Shalginbayeva, L. K. Zhumanova, “The First Regularized Trace of Integro-Differential Sturm-Liouville Operator on the Segment With Punctured Points At Integral Perturbation of Transmission Conditions”, International Conference on Analysis and Applied Mathematics ICAAM 2016, AIP Conference Proceedings, 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Physics, 2016, 020034  crossref  isi  scopus
    5. Baranets'kyi Ya.O., Kalenyuk P.I., Kolyasa L.I., “Spectral Properties of Nonself-Adjoint Nonlocal Boundary-Value Problems For the Operator of Differentiation of Even Order”, Ukr. Math. J., 70:6 (2018), 851–865  crossref  isi  scopus
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