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Year
2023
Volume
33
Issue
1
Pages
141-155
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Section Mathematics
Title On essential values of Sergeev's frequencies and exponents of oscillation for solutions of a third-order linear differential periodic equation
Author(-s) Stash A.Kh.a
Affiliations Adyghe State Universitya
Abstract In this paper, we study various types of Sergeev's frequencies and exponents of oscillation for solutions of linear homogeneous differential equations with continuous bounded coefficients. For any preassigned natural number $N$, a periodic third-order linear differential equation is constructively built in this paper, which has the property that its upper and lower Sergeev frequency spectra of strict signs, zeros and roots, as well as the spectra of all upper and lower strong and weak oscillation indices of strict and non-strict signs, zeros, roots and hyperroots contain the same set, consisting of $N$ different essential values, both metrically and topologically. Moreover, all these values are implemented on the same set of solutions of the constructed equation, that is, for each solution from this set, all the frequencies listed above and the oscillation exponents coincide with each other. When constructing the indicated equation and proving the required results, analytical methods of the qualitative theory of differential equations were used, in particular, methods of the theory of perturbations of solutions of linear differential equations, as well as the author's technique for controlling the fundamental system of solutions of such equations in one particular case.
Keywords differential equations, linear systems, oscillation, number of zeros, exponents of oscillation, Sergeev's frequencies
UDC 517.926
MSC 34C10
DOI 10.35634/vm230110
Received 9 January 2023
Language Russian
Citation Stash A.Kh. On essential values of Sergeev's frequencies and exponents of oscillation for solutions of a third-order linear differential periodic equation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 1, pp. 141-155.
References
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