Differential equations with several non-monotone arguments: An oscillation result

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

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.

Oscillation of nonlinear impulsive differential equations with piecewise constant arguments

denotes the greatest integer function, and x−1, x0 are given real numbers. Since 1980’s differential equations with piecewise constant arguments have attracted great deal of attention of researchers in mathematical and some of the others fields in science. Piecewise constant systems exist in a widely expanded areas such as biomedicine, chemistry, mechanical engineering, physics, etc. These kind...

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 ...

Oscillation Criteria for a Certain Second-order Nonlinear Differential Equations with Deviating Arguments

In this paper, by using the generalized Riccati technique and the integral averaging technique, some new oscillation criteria for certain second order retarded differential equation of the form