The Future of Differential Equations

2000 ◽  
pp. 173-176
Author(s):  
Peter D. Lax
Keyword(s):  
Differential Equations ◽  
The Future

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals On asymptotically stable sets

1970 ◽  
Vol 17 (2) ◽  
pp. 181-186 ◽  
Author(s):  
D. Desbrow
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Metric Space ◽  
Physical System ◽  
Asymptotically Stable ◽  
Stable Sets ◽  
Compact Closure ◽  
First Order ◽  
Closed Sets ◽  
The Future

In this paper we study closed sets having a neighbourhood with compact closure which are positively asymptotically stable under a flow on a metric space X. For an understanding of this and the rest of the introduction it is sufficient for the reader to have in mind as an example of a flow a system of first order, autonomous ordinary differential equations describing mathematically a time-independent physical system; in short a dynamical system. In a flow a set M is positively stable if the trajectories through all points sufficiently close to M remain in the future in a given neighbourhood of M. The set M is positively asymptotically stable if it is positively stable and, in addition, trajectories through all points of some neighbourhood of M approach M in the future.

Technology and Differential Equations

2013 ◽  
pp. 1-11
Author(s):  
John Hubbard
Keyword(s):  
Global Warming ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Mathematical Models ◽  
Real World ◽  
The Real ◽  
Greenhouse Gasses ◽  
The Future ◽  
Set Up

Differential equations are the main way in which we make mathematical models of the real world. This is true in just about all fields, from physics to fluid mechanics, from astronomy to finance: if you want to understand how something evolves, or if you want to understand equilibria, you will need to set up and “solve” differential equations. For instance, our understanding of global warming depends mainly on analyzing the differential equations modeling the weather and seeing how their behavior depends on the concentration of greenhouse gasses in the atmosphere. The future of humanity depends on our getting it right.

Reflected solutions of generalized anticipated backward double stochastic differential equations

2017 ◽  
Vol 25 (1) ◽  
Author(s):  
Liping Xu ◽  
Zhi Li ◽  
Jiaowa Luo
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Doubly Stochastic ◽  
The Future ◽  
Future Value ◽  
New Type

AbstractIn this paper, we deal with a new type of differential equations called generalized anticipated backward doubly stochastic differential equations (GA-BDSDEs). The coefficients of these BDSDEs depend on the future value of the solution

scholarly journals Models of Sexually Transmitted Diseases

2019 ◽  
Vol 4 (10) ◽  
pp. 4-8
Author(s):  
E. Soto ◽  
N. Fernandes ◽  
S. Sánchez ◽  
L. Leão ◽  
Z. Ribeiro ◽  
...  
Keyword(s):  
Qualitative Study ◽  
Differential Equations ◽  
Sexually Transmitted Diseases ◽  
General System ◽  
System Of Equations ◽  
System Of Differential Equations ◽  
Sexually Transmitted ◽  
The Future ◽  
Future Situation

In the present work a study of the situation that is presented in Brazil with regard to the sexually transmitted diseases is made, indicating those groups of people for which the most common certain diseases. It introduces a system of differential equations that simulates the process of transmission of different diseases, if different cases are studied that derive from the general system; the system is simplified according to the case, a qualitative study of the system of equations is presented and conclusions are drawn regarding the future situation in relation to the number of infested patients.

scholarly journals A model to predict COVID-19 epidemics with applications to South Korea, Italy, and Spain

2020 ◽  
Author(s):  
Z. Liu ◽  
P. Magal ◽  
Ousmane Seydi ◽  
Glenn Webb
Keyword(s):  
Differential Equations ◽  
South Korea ◽  
The World ◽  
The Future ◽  
Case Data

1AbstractIn this work, our team develops a differential equations model of COVID-19 epidemics. Our goal is to predict forward in time the future number of cases from early reported case data in regions throughout the world. Our model incorporates the following important elements of COVID-19 epidemics: (1) the number of asymptomatic infectious individuals (with very mild or no symptoms), (2) the number of symptomatic reported infectious individuals (with severe symptoms) and (3) the number of symptomatic unreported infectious individuals (with less severe symptoms). We apply our model to COVID-!9 epidemics in South Korea, Italy and Spain.

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