Geodesic
Some properties of solutions of second-order linear ordinary differential equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 69-80

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The Riccati equation method is used to obtain lower and upper estimates for the distance between two consecutive zeros of a solution and the derivative of the solution to a second-order linear ordinary differential equation in terms of its coefficients. Oscillation conditions and a stability condition are proved, and a theorem on the asymptotic behavior of zeros of solutions to a second-order linear equation and on the asymptotic behavior of one of the solutions to this equation is established.
Mots-clés : Riccati equation, oscillation, nonoscillation, oscillation on a finite interval
Keywords: estimation of the distance between two consecutive zeroes, asymptotic behavior, stability. 
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G. A. Grigoryan. Some properties of solutions of second-order linear ordinary differential equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 69-80. http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a6/