Second order linear oscillation with integrable coefficients
نویسندگان
چکیده
منابع مشابه
Oscillation and nonoscillation of solutions of second order linear differential equations with integrable coefficients
where a(t) is a locally integrable function of /. We call equation (1) oscillatory if all solutions of (1) have arbitrarily large zeros on [0, oo), otherwise, we say equation (1) is nonoscillatory. As a consequence of Sturm's Separation Theorem [21], if one of the solutions of (1) is oscillatory, then all of them are. The same is true for the nonoscillation of (1). The literature on second orde...
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We obtain Willett-Wong-type oscillation and nonoscillation theorems for second order linear dynamic equations with integrable coefficients on a time scale. The results obtained extend and are motivated by oscillation and nonoscillation results due to Willett [20] and Wong [21] for the second order linear differential equation. As applications of the new results obtained, we give the complete cl...
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Sturm and his successors! have examined in detail properties of the zeros of solutions of linear differential systems similar to (1), (3) below, and of linear combinations similar to (2). They have commonly employed the continuity and existence of derivatives of the coefficients. Under more lenient assumptions, the writer will obtain sufficient conditions that the zeros of the linear combinatio...
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In this paper, we established some sufficient conditions for the oscillation of second order neutral difference inequalities (−1)x(n) { ∆z(n) + (−1)q(n)f(x(σ(n))) } ≤ 0, n ≥ n0 (∗) where δ = 0 or δ = 1, z(n) = x(n) + p(n)x(n − τ), τ is a positive integer, {p(n)}, {q(n)} are sequences of real numbers, {σ(n)} is a sequence of nonnegative integers and f : R → R where R is the set of real numbers. ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1968
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1968-12078-6