Oscillation of third-order nonlinear neutral differential equations (original) (raw)

OSCILLATION RESULTS FOR THIRD ORDER NONLINEAR MIXED NEUTRAL DIFFERENTIAL EQUATIONS

In this paper, the authors study oscillatory and asymptotic behavior of solutions of a class of nonlinear third order neutral differential equations with positive and negative coefficients of the form a(t)(b(t)(y(t) + p(t)y(σ(t)))) + q(t)G(y(α(t))) − h(t)H(y(β(t))) = 0 (E) for 0 p(t) p 1 < 1 and −1 < p 2 p(t) 0. The results in this paper generalize the results of [LI, T.-ZHANG, C.-XING, G.: Oscillation of third-order neutral delay differential equations, Abstr. Appl. Anal. 2012 (2012), Article ID 569201] and various results in the literature. We establish new conditions which guarantees that every solutions of (E) either oscillatory or converges to zero. Examples are considered to illustrate the main results.

Oscillations of Third Order Half Linear Neutral Differential Equations

Baghdad Science Journal, 2015

In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

Oscillations of Third Order Nonlinear Neutral Differential Equations with Positive and Negative Coefficients

Mathematical Theory and Modeling, 2014

In this paper oscillation criterion is investigated for all solutions of the third-order non linear neutral differential equations with positive and negative coefficients: [ () + () ((()))]′′′ + () ((())) − () ((())) = 0, ≥ 0 (1.1) Some sufficient conditions are established so that every solution of eq.(1.1) oscillate. We improved theorem 2.4 and theorem 2.10 in [5]. Examples are given to illustrated our main results.

Oscillations of second order neutral differential equations

Mathematical and computer modelling, 1995

In this paper, we consider the oscillatory behavior of the second order neutral delay differential equation (a(t)(x(t) +p(t)x(t-r))')' + q(t)f{x(t-&)) = 0, where t>tQ,r and a are positive constants, a,p, q € C(Oo, oo), R),f G C[/?, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.

Oscillation of second order nonlinear neutral differential equations

Applied Mathematics and Computation, 2003

The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ([14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.