Abstract
In this paper, we are mainly concerned with oscillatory behavior of solutions for a class of higher odd order nonlinear neutral difference equations with continuous variable. By converting the above difference equations to the corresponding differential equations and inequalities, the oscillatory criteria are obtained. In addition, examples are given to illustrate the obtained criteria, respectively.
Highlights
1 Introduction Difference equations have attracted a great deal of attention of researchers in mathematics, biology, physics, and economy
This is specially due to the applications in various problems of biology, physics, economy
Among the topics studied for oscillation of the solutions has been investigated intensively
Summary
Difference equations have attracted a great deal of attention of researchers in mathematics, biology, physics, and economy. Throughout this paper we assume that g(t + τ ) ≥ g(t) + τ for t ≥ t and f (t, u)/u ≥ q(t) > for u = and some q ∈ C(R, R+). A function x is called the solution of In Section , some lemmas will be given to prove the main results. The following results are for the bounded solutions of Assume that p > , r = kτ , k ∈ N , r ≥ t + mτ – g(t), and rβ for some integer n ≥. Assume that τ is nondecreasing, ≤ η ≤ e– , and x(t) is an eventually positive function satisfying
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