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摘要
This paper is concerned with the oscillatory behavior of first order difference equation with general argument Delta x(n) + p(n)x (tau(n)) = 0, n = 0, 1, ... (*) where (p(n))(n >= 0) is a sequence of nonnegative real numbers and (tau(n))(n >= 0) is a sequence of integers. Let the numbers k and L be defined by k = lim inf(n ->infinity) Sigma(n-1)(j=tau(n)) p(j) and L = lim sup(n ->infinity) Sigma(n)(j=tau(n)) p(j). It is proved that, when L < 1 and 0 < k <= 1/e, all solutions of Equation (*) oscillate if the condition L > 2k + 2/lambda(1) - 1 where lambda(1) is an element of [1, e] is the unique root of the equation lambda = e(k lambda), is satisfied.
- 出版日期2015-9
