Stability criteria for systems of two first-order linear ordinary differential equations

References

[1] ADRIANOBA, L. Y.: Introduction to the Theory of Linear Systems of Differential Equations., Publishers of St. Petersburg University, S. Peterburg, 1992.Suche in Google Scholar

[2] ASHORDIA, M.: Lyapunov Stability of systems of linear generalized ordinary differential equations, Comput. Math. Appl. 50 (2005), 957–982.10.1016/j.camwa.2004.04.041Suche in Google Scholar

[3] BELLMAN, R.; Stability Theory of Differential Equations, Foreign Literature Publishers, Moscow, 1954.Suche in Google Scholar

[4] BELLMAN, R.: On an application of a Banach-Steinhaus theorem to the study of the boundedness of solutions of nonlinear differential and difference equations, Ann. Math. 49(2) (1948), 515–522.10.2307/1969041Suche in Google Scholar

[5] BURDINA, V. I.: On boundedness of solutions of systems of differential equations, Dokl. AN SSSR 93(4) (1953), 603–606.Suche in Google Scholar

[6] CEZARY, L.: Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Berlin, 1959.Suche in Google Scholar

[7] DEMIDOVICH, B. P.: Lectures on the Mathematical Stability Theory, Nauka, Moscow, 1967.Suche in Google Scholar

[8] ERBE, L. H.: Stability results for periodic second order linear differential equations, Proc. Amer. Math. Soc. 93(2) (1985), 272–276.10.1090/S0002-9939-1985-0770535-2Suche in Google Scholar

[9] FEDORIUK, M. V.: Asymptotic Methods for Linear Ordinary Differential Equations, Nauka, Moskow, 1983.Suche in Google Scholar

[10] GRIGORIAN, G. A.: On the stability of systems of two first-order linear ordinary differential equations, Differ. Equ. 51(3) (2015), 283–292.10.1134/S0012266115030015Suche in Google Scholar

[11] GRIGORIAN, G. A.: Necessary conditions and test for systems of two first-order linear ordinary differential equations, Differ. Uravn. 52(3) (2016), 289–300 (in Russian).10.1134/S0012266116030034Suche in Google Scholar

[12] GRIGORIAN, G. A.: Stability criterion for systems of two first-order linear ordinary differential equations, Math. Notes 103(6) (2018), 892–900.10.1134/S0001434618050255Suche in Google Scholar

[13] GRIGORIAN, G. A.: The behavior of solutions of the system of two first order linear ordinary differential equations, Math. Pannonica 26(1) (2017–2018), 67–101.Suche in Google Scholar

[14] GRIGORIAN, G. A.: On two comparison tests for second-order linear ordinary differential equations, Differ. Uravn. 47(9) (2011), 1225–1240 (in Russian); translation Differ. Equ. 47(9) (2011), 1237–1252.Suche in Google Scholar

[15] GRIGORIAN, G. A.: On some properties of solutions of the Riccati equation, Izvestiya NAS of Armenia 42(4) (2007), 11–26.Suche in Google Scholar

[16] GRIGORIAN, G. A.: Some properties of the solutions of linear second order ordinary differential equations, Trudy Inst. Mat. i Mekh. UrO RAN 19 (2013), 69–90.Suche in Google Scholar

[17] GRIGORIAN, G. A.: Two comparison criteria for scalar Riccati equations with applications, Russian Mathematics (Iz. VUZ) 56(11) (2012), 17–30.10.3103/S1066369X12110023Suche in Google Scholar

[18] GUSAROV, L. A.: Convergence to zero of solutions of linear second order differential equations, Doklady AN SSSR 71(1) (1950), 9–12.Suche in Google Scholar

[19] HARTMAN, PH.: Ordinary Differential Equations, 2nd ed., SIAM, 2002.10.1137/1.9780898719222Suche in Google Scholar

[20] KNOVLES, I. On stability conditions for second order linear differential equations, J. Differential Equations 34 (1979), 179–203.10.1016/0022-0396(79)90003-2Suche in Google Scholar

[21] MAC LACHLAN, N. W.: Theory and Application of Mathieu Functions, Clarendon Press, Oxford, 1947.Suche in Google Scholar

[22] SOBOL, I. M.: Study of the asymptotic behaviour of the solutions of the linear second order differential equations wit the aid of polar coordinates, Matematicheskij Sbornik 28(70) (1951), 707–714.Suche in Google Scholar

[23] YAKUBOVICH, V. A. — STARZHINSKY, V. M.: Linear Differential Equations with Periodic Coefficients and their Applications, Nauka, Moscow, 1972.Suche in Google Scholar