منابع مشابه
Survey of Oscillation Criteria for First Order Delay Differential Equations
In this paper, we discuss the oscillatory behavior of first order delay differential equations of the form: y′(t) + p(t)y(τ(t)) = 0, t ≥ T, where p and T are continuous functions defined on [T,∞), p(t) > 0, τ(t) < t for t ≥ T, τ(t) is nondecreasing and lim t→∞ τ(t) = ∞. We present best possible conditions for the oscillation of all solutions for this equation.
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Oscillation theory on Z and R has drawn extensive attention in recent years. Most of the results on Z have corresponding results on R and vice versa because there is a very close relation between Z and R. This relation has been revealed by Hilger in 1 , which unifies discrete and continuous analysis by a new theory called time scale theory. As is well known, a first-order delay differential equ...
متن کاملSome Oscillation Criteria For First Order Delay Dynamic Equations
We present an oscillation criterion for first order delay dynamic equations on time scales, which contains well-known criteria for delay differential equations and delay difference equations as special cases. We illustrate our results by applying them to various kinds of time scales.
متن کاملOscillation of Higher-order Delay Difference Equations
where {pi(n)} are sequences of nonnegative real numbers and not identically equal to zero, and ki is positive integer, i = 1,2, . . . , and is the first-order forward difference operator, xn = xn+1− xn, and xn = l−1( xn) for l ≥ 2. By a solution of (1.1) or inequality (1.2), we mean a nontrival real sequence {xn} satisfying (1.1) or inequality (1.2) for n ≥ 0. A solution {xn} is said to be osci...
متن کاملOscillation of Second Order Delay Dynamic Equations
In this paper we establish some sufficient conditions for oscillation of second order delay dynamic equations on time scales. Our results not only unify the oscillation of second order delay differential and difference equations but also are new for q-difference equations and can be applied on any time scale. We illustrate our results with many examples.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1991
ISSN: 0022-247X
DOI: 10.1016/0022-247x(91)90396-h