Oscillation of third-order nonlinear neutral differential equations (original) (raw)
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.
Oscillation results for second-order nonlinear neutral differential equations
Advances in Difference Equations, 2013
We obtain several oscillation criteria for a class of second-order nonlinear neutral differential equations. New theorems extend a number of related results reported in the literature and can be used in cases where known theorems fail to apply. Two illustrative examples are provided. MSC:34K11.
Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation
Mathematica Slovaca, 2007
In this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE) \left[ {r(t)(y(t) - p(t)y(t - \tau ))'} \right]^\prime + q(t)G(y(h(t))) = 0$$ are obtained, where q, h ∈ C([0, ∞), ℝ) such that q(t) ≥ 0, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C ([0, ∞), ℝ), G ∈ C (ℝ, ℝ) and τ ∈ ℝ+. Since the results of this paper hold when r(t) ≡ 1 and G(u) ≡ u, therefore it extends, generalizes and improves some known results.
Research Article Oscillatory Behavior of Second-Order Nonlinear Neutral Differential Equations
We study oscillatory behavior of solutions to a class of second-order nonlinear neutral differential equations under the assumptions that allow applications to differential equations with delayed and advanced arguments. New theorems do not need several restrictive assumptions required in related results reported in the literature. Several examples are provided to show that the results obtained are sharp even for second-order ordinary differential equations and improve related contributions to the subject.
Asymptotic and oscillatory characteristics of solutions of neutral differential equations
Journal of Mathematics and Computer Science, 2025
The paper investigates third-order linear neutral differential equations in the non-canonical case, aiming to simplify the complexity of such equations by transforming them into the canonical form. This transformation reduces the number of potential cases for positive solutions and their derivatives from four in the non-canonical case to two in the canonical case, significantly facilitating the derivation of results. Using an iterative method, we establish conditions that exclude the existence of positive solutions fulfilling the equation. Furthermore, by employing a comparison approach with first-order equations, we derive additional conditions that exclude the existence of Kneser-type solutions that satisfy the equation. By combining these conditions, we derive new oscillation criteria that guarantee the oscillation of all solutions satisfying the studied equation. Our findings extend and generalize existing results in the literature. We provide three illustrative examples to demonstrate our results' validity and significance.