Existence of non-oscillatory solutions of a kind of first-order neutral differential equation

This paper deals with the existence of non-oscillatory solutions to a kind of first-order neutral equations having both delay and advance terms. The new results are established using the Banach contraction principle

Differential/Difference Equations

The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations

Properties of Third-Order Nonlinear Functional Differential Equations with Mixed Arguments

The aim of this paper is to offer sufficient conditions for property (B) and/or the oscillation of the third-order nonlinear functional differential equation with mixed arguments [()[″()]]′=()([()])+()ℎ([()]). Both cases ∫∞−1/()d=∞ and ∫∞−1/()d<∞ are considered. We deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones

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

Necessary and sufficient conditions for the oscillation of higher-order differential equations involving distributed delays

In this article, we establish necessary and sufficient conditions for the oscillation of both bounded and unbounded solutions of the differential equation \begin{equation} \bigg[x(t)+\int_{0}^{\lambda}p(t,v)x(\tau(t,v))\,\mathrm{d}v\bigg]^{(n)}+\int_{0}^{\lambda}q(t,v)x(\sigma(t,v))\,\mathrm{d}v=\varphi(t)\quad\text{for } t \geq t_{0},\notag \end{equation} where $n\in\mathbb{N}$, $t_{0},\lambda\in\mathbb{R}^{+}$, $p\in C([t_{0},\infty)\times[0,\lambda] \mathbb{R})$, $q\in C([t_{0},\infty)\times[0,\lambda],\mathbb{R}^{+})$, $\tau\in C([t_{0},\infty)\times[0 \lambda],\mathbb{R})$ with $\lim_{t\to\infty}\inf_{v\in[0,\lambda]}\tau(t,v)=\infty$ and $\sup_{v\in[0,\lambda]}\tau(t,v)\leq t$ for all $t\geq t_{0}$, $\sigma\in C([t_{0},\infty)\times[0,\lambda],\mathbb{R})$ with $\lim_{t\to\infty}\inf_{v\in[0,\lambda]}\sigma(t,v)=\infty$, and $\varphi\in C([t_{0},\infty),\mathbb{R})$. We also give illustrating examples to show the applicability of these results

Asymptotics and Hille-Type Results for Dynamic Equations of Third Order with Deviating Arguments

The aim of this paper is to deduce the asymptotic and Hille-type criteria of the dynamic equations of third order on time scales. Some of the presented results concern the sufficient condition for the oscillation of all solutions of third-order dynamical equations. Additionally, compared with the related contributions reported in the literature, the Hille-type oscillation criterion which is derived is superior for dynamic equations of third order. The symmetry plays a positive and influential role in determining the appropriate type of study for the qualitative behavior of solutions to dynamic equations. Some examples of Euler-type equations are included to demonstrate the finding. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Acknowledgments: This research has been funded by Scientific Research Deanship at University of Ha’il—Saudi Arabia through project number RG-20 125