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Defect basis property of a system of root functions of a Sturm–Liouville problem with spectral parameter in the boundary conditions

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Abstract

We consider a Sturm–Liouville problem with spectral parameter in the boundary conditions. We give a general characteristic of the arrangement of eigenvalues on the real axis (the complex plane), study the structure of root subspaces and the oscillation properties of eigenfunctions, and analyze the basis properties of systems of root functions of this problem in the space L p (0, 1), 1 < p < ∞.

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Authors and Affiliations

  1. Baku State University, Baku, Azerbaijan

    Z. S. Aliev & A. A. Dun’yamalieva

  2. Institute for Mathematics and Mechanics, National Academy of Sciences, Baku, Azerbaijan

    Z. S. Aliev & A. A. Dun’yamalieva

Authors
  1. Z. S. Aliev
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  2. A. A. Dun’yamalieva
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Correspondence to Z. S. Aliev.

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Original Russian Text © Z.S. Aliev, A.A. Dun’yamalieva, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 10, pp. 1259–1276.

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Aliev, Z.S., Dun’yamalieva, A.A. Defect basis property of a system of root functions of a Sturm–Liouville problem with spectral parameter in the boundary conditions. Diff Equat 51, 1249–1266 (2015). https://doi.org/10.1134/S0012266115100018

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  • DOI: https://doi.org/10.1134/S0012266115100018

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