An oscillation criterion for delay differential equations with several non-monotone arguments

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

An Oscillation Criterion for Nonlinear Third-order Differential Equations

Sufficient conditions for oscillation of a certain class of nonlinear third-order differential equations are found. In this paper we considear a nonlinear third-order differential equation of the form y′′′ + q(t)y′ = f(t, y, y′, y′′) (1) where (i) q, q′ ∈ C ( (a,∞) ) for some a with 0 < a < ∞, (ii) f ∈ C ( (a,∞)×R3 ) , t ∈ (a,∞), and y1, y2, y3 ∈ R and f(t, y1, y2, y3)y1 < 0 for all t ∈ (a,∞) a...

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...

Oscillation for second order nonlinear delay differential equations with impulses

In this paper , we investigate the oscillation of second order nonlinear delay differential equations with impulses of the form k k k k k k k r t x t p t x t Q t x t t t t t k n x t g x t x t h x t