Oscillatory and Nonoscillatory Behaviorof Second -
نویسنده
چکیده
|For the diierence equation (pn(yn + hn y n?k)) + q n+1 f (y n+1?`) = 0; the existence of solutions in the classes M + , M ? , and WOS is established.
منابع مشابه
Oscillation and nonoscillation criteria for half-linear second order di¤erential equations
We investigate oscillatory properties of the second order half-linear differential equation ðrðtÞFðy 0ÞÞ 0 þ cðtÞFðyÞ 1⁄4 0; FðsÞ :1⁄4 jsj s; p > 1; ð*Þ viewed as a perturbation of a nonoscillatory equation of the same form ðrðtÞFðy 0ÞÞ 0 þ ~ cðtÞFðyÞ 1⁄4 0: Conditions on the di¤erence cðtÞ ~ cðtÞ are given which guarantee that equation ð*Þ becomes oscillatory (remains nonoscillatory).
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Nonoscillatory second order differential equations always admit “special”, principal solutions. For a certain type of oscillatory equation principal pairs of solutions were introduced by Á. Elbert, F. Neuman and J. Vosmanský, Diff. Int. Equations 5 (1992), 945–960. In this paper, the notion of principal pair is extended to a wider class of oscillatory equations. Also an interesting property of ...
متن کاملPrincipal Pairs for Oscillatory Second Order Linear Differential Equations
Nonoscillatory second order differential equations always admit “special”, principal solutions. For a certain type of oscillatory equation principal pairs of solutions were introduced by Á. Elbert, F. Neuman and J. Vosmanský, Diff. Int. Equations 5 (1992), 945–960. In this paper, the notion of principal pair is extended to a wider class of oscillatory equations. Also an interesting property of ...
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and Applied Analysis 3 In 10 , Leighton proved the following well-known oscillation test for 1.4 ; see 10, 11 . Theorem A see 10 . Assume that ∫∞ t0 1 A0 ( η )dη ∞, ∫∞ t0 A1 ( η ) dη ∞, 1.5 then 1.3 is oscillatory. This result for 1.4 was obtained by Wintner in 12 without imposing any sign condition on the coefficient A1. In 13 , Kneser proved the following result. Theorem B see 13 . Equation 1...
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