Iterative oscillation tests for difference equations with several non-monotone arguments

Oscillations of difference equations with non-monotone retarded arguments

Keyword: Difference equation Non-monotone argument Retarded argument Oscillatory solutions Nonoscillatory solutions Consider the first-order retarded difference equation DxðnÞ þ pðnÞx sðnÞ ð Þ 1⁄4 0; n 2 N0 where ðpðnÞÞnP0 is a sequence of nonnegative real numbers, and ðsðnÞÞnP0 is a sequence of integers such that sðnÞ 6 n 1, n P 0; and limn!1 sðnÞ 1⁄4 1. Under the assumption that the retarded ...

New oscillation criterion for delay differential equations with non-monotone arguments

Oscillation Criteria for Difference Equations with Several Oscillating Coefficients

This paper presents a new sufficient condition for the oscillation of all solutions of difference equations with several deviating arguments and oscillating coefficients. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.

Linearized Oscillation of Nonlinear Difference Equations with Advanced Arguments

This paper is concerned with the nonlinear advanced difference equation with constant coefficients

Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II

We study the oscillation of solutions to the differential equation ẋ(t) + a1(t)x[r(t)] + a2(t)x[p(t)] = 0, t ≥ t0 which has a retarded argument r(t) and an advanced argument p(t). We obtain oscillation and non-oscillation conditions which are closed to be necessary. We provide examples to show that our results are best possible and compare them with known results.