Journal of Mathematical Sciences

, Volume 217, Issue 2, pp 176–186 | Cite as

Nonlocal Multipoint Problem for Differential-Operator Equations of Order 2n

  • Ya. O. Baranetskij
  • A. A. Basha

We study a nonlocal multipoint problem for differential-operator equations of order 2n.The spectral properties of the operator of this problem are analyzed and the conditions for the existence and uniqueness of its solution are established. The solution of the problem is found in the form of expansion in series in the system of eigenfunctions. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ya. O. Baranetskij, P. I. Kalenyuk, and U. B. Yarka, “Perturbation of boundary-value problems for second-order ordinary differential equations,” Visnyk Derzh. Univ. “L’viv. Politekhnika,” Ser. Prykl. Matem., 1, No. 337, 70–73 (1998).Google Scholar
  2. 2.
    Ya. O. Baranetskij and U. B. Yarka, “On a class of boundary-value problems for even-order differential-operator equations,” Mat. Met. Fiz.-Mekh. Polya, 42, No. 4, 64–67 (1999).Google Scholar
  3. 3.
    N. K. Bari, “Biorthogonal systems and bases in a Hilbert space,” Uchen. Zapiski Mosk. Gos. Univ., 4, No. 148, 69–107 (1951).MathSciNetGoogle Scholar
  4. 4.
    V. I. Gorbachuk and M. L. Gorbachuk, Boundary-Value Problems for Differential-Operator Equations [in Russian], Naukova Dumka, Kiev (1984).zbMATHGoogle Scholar
  5. 5.
    I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Nonself-Adjoint Operators in Hilbert Spaces [in Russian], Nauka, Moscow (1965).Google Scholar
  6. 6.
    P. I. Kalenyuk, Ya. E. Baranetskij, and Z. N. Nitrebich, Generalized Method of Separation of Variables [in Russian], Naukova Dumka, Kiev (1993).Google Scholar
  7. 7.
    V. P. Kurdyumov and A. P. Khromov, “On Riesz bases of the eigenfunctions and adjoint functions of a differential-difference operator with multipoint boundary conditions,” in: Mathematics. Mechanics: Collection of Scientific Works [in Russian], Issue 6, Izd. Saratov Univ., Saratov (2004), pp. 80–82.Google Scholar
  8. 8.
    V. P. Mikhailov, “On Riesz bases in Open image in new window (0,1),” Dokl. Akad. Nauk SSSR, 144, No. 5, 981–984 (1962).Google Scholar
  9. 9.
    D. Jakobson, M. Levitin, N. Nadirashvili, and I. Polterovich, “Spectral problems with mixed Dirichlet–Neumann boundary conditions: isospectrality and beyond,” J. Comput. Appl. Math., Special issue on 60th birthday of Prof. Brian Davies, 194, No. 1, 141–155 (2006).Google Scholar
  10. 10.
    A. Kopzhassarova and A. Sarsenbi, ”Basis properties of eigenfunctions of second-order differential operators with involution,” Abstr. Appl. Anal., 2012, Article ID 576843 (2012), pp. 1–6.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Ya. O. Baranetskij
    • 1
  • A. A. Basha
    • 1
  1. 1.L’vivs’ka Politekhnika” National UniversityLvivUkraine

Personalised recommendations