Differential Equations

, Volume 46, Issue 4, pp 509–514

Unconditional bases related to a nonclassical second-order differential operator

  • A. M. Sarsenbi
Ordinary Differential Equations

DOI: 10.1134/S0012266110040051

Cite this article as:
Sarsenbi, A.M. Diff Equat (2010) 46: 509. doi:10.1134/S0012266110040051


In the present paper, we introduce the notion of regularity of boundary conditions for a simplest second-order differential equation with a deviating argument. We prove the Riesz basis property for a system of root vectors of the corresponding generalized spectral problem with regular boundary conditions (in the sense of the introduced definition). Examples of irregular boundary conditions to which the theory of Il’in basis property can be applied are given.

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. M. Sarsenbi
    • 1
  1. 1.South-Kazakhstan State UniversityShymkentKazakhstan