Dynamics of Third-Order Nonlinear Neutral Equations

Oscillation of third-order nonlinear neutral differential equations

With the development of modern society, research on properties of ordinary differential equation is becoming one of the hotspots in mathematical field. Neutral differential equation which is usually generated in natural science and engineering field is always extensively concerned by many scientific researchers for it can effectively describe multiple complex phenomena in natural world. In rece...

Oscillation Criteria of Third Order Nonlinear Neutral Difference Equations

In this paper we consider the third order nonlinear neutral difference equation of the form ∆(rn(∆(xn ± pnxσ(n)))) + f (n, xτ(n)) = 0, we establish some sufficient conditions which ensure that every solution of this equation are either oscillatory or converges to zero. Examples are provided to illustrate the main results.

Nonlinear oscillation of certain third-order neutral differential equation with distributed delay

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...

Oscillation of Third-Order Neutral Delay Differential Equations

and Applied Analysis 3 Theorem 2.1. Assume that 1.4 holds, 0 ≤ p t ≤ p1 < 1. If for some function ρ ∈ C1 t0,∞ , 0,∞ , for all sufficiently large t1 ≥ t0 and for t3 > t2 > t1, one has lim sup t→∞ ∫ t t3 ⎛ ⎜⎝ρ s q s (1 − p τ s ) ∫τ s t2 (∫v t1 1/a u du/b v ) dv ∫s t1 1/a u du − a s ( ρ′ s )2 4ρ s ⎞ ⎟⎠ds ∞, 2.1 ∫∞

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS