An Improved Oscillation Result for a Class of Higher Order Non-canonical Delay Differential Equations.

[EN]In this work, by obtaining a new condition that excludes a class of positive solutions of a type of higher order delay differential equations, we were able to construct an oscillation criterion that simplifies, improves and complements the previous results in the literature. The adopted approach extends those commonly used in the study of second-order equations. The simplification lies in obtaining an oscillation criterion with two conditions, unlike the previous results, which required at least three conditions. In addition, we illustrate the improvement with the new criterion, applying it to some examples and comparing the results obtained with previous results in the literature

Sufficient conditions for oscillation of fourth-order neutral differential equations with distributed deviating arguments

Some new sufficient conditions are established for the oscillation of fourth-order neutral differential equations with continuously distributed delay. An example is provided to show the importance of these resul

Improved results for testing the oscillation of functional differential equations with multiple delays

In this article, we test whether solutions of second-order delay functional differential equations oscillate. The considered equation is a general case of several important equations, such as the linear, half-linear, and Emden-Fowler equations. We can construct strict criteria by inferring new qualities from the positive solutions to the problem under study. Furthermore, we can incrementally enhance these characteristics. We can use the criteria more than once if they are unsuccessful the first time thanks to their iterative nature. Sharp criteria were obtained with only one condition that guarantees the oscillation of the equation in the canonical and noncanonical forms. Our oscillation results effectively extend, complete, and simplify several related ones in the literature. An example was given to show the significance of the main results

Oscillation theorems for fourth-order quasi-linear delay differential equations

In this paper, we deal with the asymptotic and oscillatory behavior of quasi-linear delay differential equations of fourth order. We first find new properties for a class of positive solutions of the studied equation, $\mathcal{N}_{a}$. As an extension of the approach taken in [1], we establish a new criterion that guarantees that $\mathcal{N}_{a} = \emptyset$. Then, we create a new oscillation criterion

Burnout among surgeons before and during the SARS-CoV-2 pandemic: an international survey

Background: SARS-CoV-2 pandemic has had many significant impacts within the surgical realm, and surgeons have been obligated to reconsider almost every aspect of daily clinical practice. Methods: This is a cross-sectional study reported in compliance with the CHERRIES guidelines and conducted through an online platform from June 14th to July 15th, 2020. The primary outcome was the burden of burnout during the pandemic indicated by the validated Shirom-Melamed Burnout Measure. Results: Nine hundred fifty-four surgeons completed the survey. The median length of practice was 10 years; 78.2% included were male with a median age of 37 years old, 39.5% were consultants, 68.9% were general surgeons, and 55.7% were affiliated with an academic institution. Overall, there was a significant increase in the mean burnout score during the pandemic; longer years of practice and older age were significantly associated with less burnout. There were significant reductions in the median number of outpatient visits, operated cases, on-call hours, emergency visits, and research work, so, 48.2% of respondents felt that the training resources were insufficient. The majority (81.3%) of respondents reported that their hospitals were included in the management of COVID-19, 66.5% felt their roles had been minimized; 41% were asked to assist in non-surgical medical practices, and 37.6% of respondents were included in COVID-19 management. Conclusions: There was a significant burnout among trainees. Almost all aspects of clinical and research activities were affected with a significant reduction in the volume of research, outpatient clinic visits, surgical procedures, on-call hours, and emergency cases hindering the training. Trial registration: The study was registered on clicaltrials.gov "NCT04433286" on 16/06/2020

On the Oscillatory Behavior of a Class of Fourth-Order Nonlinear Differential Equation

In this work, we study the oscillatory behavior of a class of fourth-order differential equations. New oscillation criteria were obtained by employing a refinement of the Riccati transformations. The new theorems complement and improve a number of results reported in the literature. An example is provided to illustrate the main results

Asymptotic Behavior of Solutions of Even-Order Differential Equations with Several Delays

The higher-order delay differential equations are used in the describing of many natural phenomena. This work investigates the asymptotic properties of the class of even-order differential equations with several delays. Our main concern revolves around how to simplify and improve the oscillation parameters of the studied equation. For this, we use an improved approach to obtain new properties of the positive solutions of these equations

An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type

It is easy to notice the great recent development in the oscillation theory of neutral differential equations. The primary aim of this work is to extend this development to neutral differential equations of mixed type (including both delay and advanced terms). In this work, we consider the second-order non-canonical neutral differential equations of mixed type and establish a new single-condition criterion for the oscillation of all solutions. By using a different approach and many techniques, we obtain improved oscillation criteria that are easy to apply on different models of equations

Asymptotic and Oscillatory Properties of Noncanonical Delay Differential Equations

In this work, by establishing new asymptotic properties of non-oscillatory solutions of the even-order delay differential equation, we obtain new criteria for oscillation. The new criteria provide better results when determining the values of coefficients that correspond to oscillatory solutions. To explain the significance of our results, we apply them to delay differential equation of Euler-type

Dynamics of difference equation xn+1=f(xn−l,xn−k) xn+1=f(xn−l,xn−k)x_{n+1}=f( x_{n-l},x_{n-k})

Abstract In this paper, we present the asymptotic behavior of the solutions for a general class of difference equations. We introduce general theorems in order to study the stability and periodicity of the solutions. Moreover, we use a new technique to study the existence of periodic solutions of this general equation. By using our general results, we can study many special cases that have not been studied previously and some problems that were raised previously. Some numerical examples are provided to illustrate the new results