Oscillation Criteria for Second-Order Nonlinear Neutral Delay Differential Equations (original) (raw)

New oscillation criteria for second-order nonlinear neutral delay differential equations

2009

In this paper, several new oscillation criteria for the second-order nonlinear neutral delay differential equation [r(t)|(x(t)+p(t)x[@s(t)])^'|^m^-^1(x(t)+p(t)x[@s(t)])^']^'+q(t)f(x[@t(t)])=0,t>=t"0 are established. These oscillation criteria extend and improve some known results. An interesting example illustrating the importance of our results is also provided.

On oscillatory nonlinear second order neutral delay differential equations

Differential Equations and Applications, 2016

In this work, we investigate the oscillation criteria for second order neutral delay differential equations of the form (r(t)[y(t) + p(t)y(δ (t))]) + q(t)G(y(τ(t))) = 0 and (r(t)[[y(t) + p(t)y(δ (t))] ] α) + q(t)(y β (τ(t))) = 0, where α and β are the ratio of odd positive integers.

On oscillatory second-order nonlinear delay differential equations of neutral type

Open Journal of Mathematical Sciences

In this paper, new sufficient conditions are obtained for oscillation of second-order neutral delay differential equations of the form d dt r(t) d dt x(t) + p(t)x(t − τ) + q(t)G x(t − σ 1) + v(t)H x(t − σ 2) = 0, t ≥ t 0 , under the assumptions ∞ 0 dη r(η) = ∞ and ∞ 0 dη r(η) < ∞ for |p(t)| < +∞. Two illustrative examples are included.

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.

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 RESULTS FOR SECOND ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH DELAY

In this paper, oscillatory and asymptotic behavior of solutions of a class of nonlinear second order neutral differential equations with positive and negative coefficients of the form (r 1 (t)(x(t) + p 1 (t)x(τ (t)))) + r 2 (t)(x(t) + p 2 (t)x(σ(t))) +p(t)G(x(α(t))) − q(t)H(x(β(t))) = 0 and (r 1 (t)(x(t) + p 1 (t)x(τ (t)))) + r 2 (t)(x(t) + p 2 (t)x(σ(t))) +p(t)G(x(α(t))) − q(t)H(x(β(t))) = f (t) are studied for various ranges of p 1 (t), p 2 (t).

Sharp results for oscillation of second-order neutral delay differential equations

Electronic Journal of Qualitative Theory of Differential Equations

The aim of the present paper is to continue earlier works by the authors on the oscillation problem of second-order half-linear neutral delay differential equations. By revising the set method, we present new oscillation criteria which essentially improve a number of related ones from the literature. A couple of examples illustrate the value of the results obtained.