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On Basic Properties of Eigenfunctions and Associated Functions of One Loaded Operator of Multiple Differentiation

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Abstract

In this paper, we consider perturbations of a second-order differential equation for a spectral problem with a loaded term containing a value of derivative of the desired function at the zero point, with regular, but not strongly regular, boundary value conditions. A characteristic determinant of the considered spectral problem is constructed. Question on stability and instability of basis property of systems of root functions of a loaded second-order differential operator is investigated.

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Funding

The research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09260752)

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Authors and Affiliations

  1. South Kazakhstan State Pedagogical University, Shymkent, Kazakhstan

    N. S. Imanbaev

  2. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    N. S. Imanbaev

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  1. N. S. Imanbaev
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Correspondence to N. S. Imanbaev.

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(Submitted by T. K. Yuldashev)

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Imanbaev, N.S. On Basic Properties of Eigenfunctions and Associated Functions of One Loaded Operator of Multiple Differentiation. Lobachevskii J Math 43, 749–754 (2022). https://doi.org/10.1134/S1995080222060117

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  • DOI: https://doi.org/10.1134/S1995080222060117

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