Distribution of eigenvalues of a perturbed differentiation operator on the interval

Year 2023, Volume: 5 Issue: 2, 24 - 31, 30.11.2023

Nurlan Imanbaev

https://doi.org/10.47087/mjm.1333727

Abstract

In this paper, we construct a characteristic determinant of the spectral problem of a first-order differential equation on an interval with an integral perturbation in the boundary value condition, which is an entire analytic function of the spectral parameter. Based on the formula for the characteristic determinant, conclusions are drawn about the asymptotic behavior of the spectrum of the perturbed spectral problem depending on the modulus of continuity of the subinteral function.

Keywords

differentiation operator, continuous functions, entire functions, boundary value conditions, integral perturbation, characteristic determinant, eigenvalues, zeros, asymptotics, continuity module, loaded differential equation.

Supporting Institution

Kazakhstan

Project Number

Kazakhstan

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