Abstract
For the system y′=b(x) z, z′=−a (x)y, wherea (x), b(x)) ∈ c [x0+∞), b(x)⩾ 0 we obtain for x≥x0a necessary and sufficient condition for nonoscillatory behavior. From this condition we derive new criteria for the nonoscillatory behavior of the system considered.
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P. Hartman, Ordinary Differential Equations, Wiley, New York (1964).
A. Wintner, “On the nonexistence of conjugate points,” Amer. J. Math.,73, No. 2, 368–380 (1951).
I. V. Kamenev, “On an integral comparison of two linear second-order differential equations,” Uspekhi Matem. Nauk,27, No. 3, 199–200 (1972).
I. V. Kamenev, “An integral comparison theorem for certain systems of linear differential equations,” Differents. Uravnen.,8, No. 5, 778–784 (1972).
V. A. Kondrat'ev, “Sufficient conditions for the nonoscillation and oscillation of the solutions of the equations y″+p(x)y=0,” Dokl. Akad. Nauk SSSR,113, No. 4, 742–745 (1957).
I. V. Kamenev, “Nonoscillation of the solutions of a linear second-order differential equation,” Differents. Uravnen.,8, No. 6, 1108–1110 (1972).
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Translated from Matematicheskie Zametki, Vol. 16, No. 2, pp. 259–265, August, 1974.
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Kamenev, I.V. A necessary and sufficient condition for nonoscillatory behavior of the solutions of a system of two linear equations of the first order. Mathematical Notes of the Academy of Sciences of the USSR 16, 742–746 (1974). https://doi.org/10.1007/BF01105581
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DOI: https://doi.org/10.1007/BF01105581