George E. Chatzarakis

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It is well known that the linear differential equation ˙ x(t) + p(t)x(t − τ(t)) = 0 a positive solution on [t 0 , ∞) if an explicit criterion of the integral type t t−τ(t) p(s)ds ≤ 1 e holds for all t ∈ [t 0 , ∞). In this paper new integral explicit criteria, which essentially supplement related results in the literature are established. For example, if,(More)
Keyword: Difference equation Non-monotone argument Retarded argument Oscillatory solutions Nonoscillatory solutions a b s t r a c t Consider the first-order retarded difference equation DxðnÞ þ pðnÞx sðnÞ ð Þ¼0; n 2 N 0 where ðpðnÞÞ nP0 is a sequence of nonnegative real numbers, and ðsðnÞÞ nP0 is a sequence of integers such that sðnÞ 6 n À 1, n P 0; and lim(More)