Spectra of Total and Vector Frequencies of Third-Order Linear Differential Equations
For any positive integer N, we construct a linear third-order differential equation with periodic coefficients whose nontrivial solutions have at least N different total (vector) frequencies. Moreover, we construct a linear third-order differential equation with bounded variable coefficients whose nontrivial solutions have countably many total (vector) frequencies.
KeywordsNontrivial Solution Small Interval Total Frequency Fundamental System Adjacent Element
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- 2.I. N. Sergeev, “Properties of the characteristic frequencies of linear equations of arbitrary order,” Tr. Semin. Petrovskogo, 29, 414–442 (2013).Google Scholar
- 4.D. S. Burlakov and S. V. Tsoi, “Coincidence of total and vector frequencies of solutions of linear autonomous systems,” Differ. Uravn., 47, No. 11, 1662–1663 (2011).Google Scholar
- 5.A. Kh. Stash, “Spectra of total and vector frequencies of third-order linear differential equations,” Differ. Uravn., 48, No. 6, 908 (2012).Google Scholar
- 6.A. Kh. Stash, “On the set of values of total frequencies of solutions of a linear equation,” Differ. Uravn., 47, No. 11, 1665 (2011).Google Scholar
- 7.I. N. Sergeev, “Control of solutions of a linear differential equation,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 3, 25–33 (2009).Google Scholar