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$N$th order extension of the Wintner-Leighton theorem. (English) Zbl 1030.34030
Summary: Sufficient conditions are given for the existence of oscillatory and nonoscillatory solutions to a class of $n$th-order linear differential equations. These results include an extension of the Wintner-Leighton theorem.

##### MSC:
 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
##### Keywords:
existence; solutions; Wintner-Leighton theorem
Full Text:
##### References:
 [1] J. Barret, Oscillating theory of ordinary differential equations, Adv. Math. 3 (1969) [2] W. Coppel, Disconjugacy, Lecture Notes in Mathematics, vol. 220, Springer, Berlin, 1971 [3] M. Gregus, Third Order Linear Differential Equations, Reidel, Dordrecht, 1987 [4] W. Leighton, On self-adjoint differential equations of second order, J. London Math. Soc. 27 (1952) · Zbl 0048.06503 [5] G. Polya, On the Mean Value Theorem corresponding to a given linear homogeneous differential equation, Trans. Am. Math. Soc. 24 (1924) [6] W.T. Reid, Ordinary Differential Equations, Wiley, New York, 1971 · Zbl 0212.10901 [7] C. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Academic Press, New York, 1968 · Zbl 0191.09904 [8] B. Travis, R. Navarro, On Sturmian theory, to appear in Dynamics of Continuous, Implusive, and Discrete Systems [9] D. Willet, Classification of second order differential equations with respect to oscillation, Adv. Math. 3 (1969) [10] A. Wintner, A criterion of oscillation stability, Q. Appl. Math. 7 (1949) · Zbl 0032.34801