Abstract
We indicate a linear homogeneous two-dimensional differential system with continuous unbounded coefficients whose sets of exact total (vector) frequencies of signs, zeros, and roots of nonzero solutions fill one and the same closed interval.
References
Sergeev, I.N., The Determination and Properties of Characteristic Frequencies of Linear Equations, Tr. Semin. im. I.G. Petrovskogo, 2006, vol. 25, pp. 249–294.
Sergeev, I.N., Properties of Characteristic Frequencies of Linear Equations of an Arbitrary Order, Tr. Semin. im. I.G. Petrovskogo, 2012, vol. 29, pp. 414–442.
Sergeev, I.N., Definition of Total Frequencies of Solutions of a Linear System, Differ. Uravn., 2009, vol. 45, no. 6, p. 908.
Sergeev, I.N., A Remarkable Coincidence of Oscillatory and Wandering Characteristics of Solutions of Differential Systems, Mat. Sb., 2013, vol. 204, pp. 119–138.
Sergeev, I.N., Oscillation and Wandering of Solutions of a Second-Order Differential Equation, Vestn. Moskov. Univ. Ser. I Mat. Mekh., 2011, no. 6, pp. 21–26.
Stash, A.Kh., On the Existence of a Linear Differential Equation of the Third Order with Continual Spectra of Total and Vector Frequencies, Vestn. Adyg. Gos. Univ. Estestv.-Mat. Tekhn. Nauki, 2013, vol. 3 (122), pp. 9–17.
Goritskii, A.Yu. and Fisenko, T.N., Characteristic Frequencies of Zeros of a Sum of Two Harmonic Oscillations, Differ. Uravn., 2012, vol. 48, no. 4, pp. 479–486.
Smolentsev, M.V., Existence of a Periodic Linear Differential Equation of the Third Order with Continual Spectrum of Frequencies, Differ. Uravn., 2012, vol. 48, no. 11, pp. 1571–1572.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.Kh. Stash, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 1, pp. 143–144.
Rights and permissions
About this article
Cite this article
Stash, A.K. Existence of a two-dimensional linear system with continual spectra of total and vector frequencies. Diff Equat 51, 146–148 (2015). https://doi.org/10.1134/S0012266115010164
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266115010164