Oscillation Criteria for Second‐Order Neutral Damped Differential Equations with Delay Argument

The chapter is devoted to study the oscillation of all solutions to second‐order nonlinear neutral damped differential equations with delay argument. New oscillation criteria are obtained by employing a refinement of the generalized Riccati transformations and integral averaging techniques

Sharp results for oscillation of second-order neutral delay 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

A sharp oscillation result for second-order half-linear non canonical delay differential equations

In the paper, new single-condition criteria for the oscillation of all solutions to a second-order half-linear delay differential equation in noncanonical form are obtained, relaxing a traditionally posed assumption that the delay function is nondecreasing. The oscillation constant is best possible in the sense that the strict inequality cannot be replaced by the nonstrict one without affecting the validity of the theorem. This sharp result is new even in the linear case and, to the best of our knowledge, improves all the existing results reporting in the literature so far. The advantage of our approach is the simplicity of the proof, only based on sequentially improved monotonicities of a positive solution

New oscillation results to fourth order delay differential equations with damping

This paper is concerned with the oscillation of the linear fourth order delay differential equation with damping \begin{equation*} \left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)'+p(t)y'(t)+q(t)y(\tau(t))=0 \end{equation*} under the assumption that the auxiliary third order differential equation \begin{equation*} \left(r_3(t)\left(r_2(t)z'(t)\right)'\right)'+\frac{p(t)}{r_1(t)}z(t)=0 \end{equation*} is nonoscillatory. In addition, a couple of examples is provided to illustrate the relevance of the main results

Asymptotic Properties of Kneser Solutions to Third-Order Delay Differential Equations

The aim of this paper is to extend and complete the recent work by Graef et al. (J. Appl. Anal. Comput., 2021) analyzing the asymptotic properties of solutions to third-order linear delay differential equations. Most importantly, the authors tackle a particularly challenging problem of obtaining lower estimates for Kneser-type solutions. This allows improvement of existing conditions for the nonexistence of such solutions. As a result, a new criterion for oscillation of all solutions of the equation studied is established

OSCILLATION of SECOND-ORDER HALF-LINEAR NEUTRAL NONCANONICAL DYNAMIC EQUATIONS

In This Paper, We Shall Establish Some New Criteria for the Oscillation of Certain Second-Order Noncanonical Dynamic Equations with a Sublinear Neutral Term. This Task is Accomplished by Reducing the Involved Nonlinear Dynamic Equation to a Second-Order Linear Dynamic Inequality. We Also Establish Some New Oscillation Theorems Involving Certain Integral Conditions. Three Examples, Illustrating Our Results, Are Presented. Our Results Generalize Results for Corresponding Differential and Difference Equations

Nonoscillatory Solutions of Higher-Order Fractional Differential Equations

This paper deals with the asymptotic behavior of the nonoscillatory solutions of a certain forced fractional differential equations with positive and negative terms, involving the Caputo fractional derivative. The results obtained are new and generalize some known results appearing in the literature. Two examples are also provided to illustrate the results

On asymptotic properties of solutions to third-order delay differential equations

We study some relations between canonical and strongly noncanonical operators, showing the advantage of this reverse approach based on the use of a noncanonical representation of L3 in the study of oscillatory and asymptotic properties of third-order delay differential equations

Oscillation criteria for second-order neutral delay differential equations

New sufficient conditions for oscillation of second-order neutral half-linear delay differential equations are given. Our results essentially improve, complement and simplify a number of related ones in the literature, especially those from a recent paper [R. P. Agarwal, Ch. Zhang, T. Li, Appl. Math. Comput. 274(2016), 178–181.]. An example illustrates the value of the results obtained