Nonlinear Differential Equations of the Automatic Regulation System Having a Single Regulating Member

ARS Journal ◽  
1961 ◽  
Vol 31 (1) ◽  
pp. 102-116
Author(s):  
V. A. YAKUBOVICH
Author(s):  
А. Yu. Izmaylov ◽  
Ya. P. Lobachevskiy ◽  
V. К. Khoroshenkov ◽  
N. Т. Goncharov ◽  
S. E. Lonin ◽  
...  

The introduction of information and digital technologies that support and support all technological processes in the field is an urgent need for the development and implementation of such technology. An organisationally complex and financially intensive project is necessary because of the wide variety of economic entities that differ in the size of production, forms of ownership and socio-economic conditions of production. Automated information control system for mobile units agricultural enterprise provides those-Niko-economic performance, optimum capacity utilization through the use of timely and reliable information on technology. Machine and tractor aggregates are appertained as control objects with variable structure, which is explained by possibility of the system formation from tractor or field machines mobile units with various purposes: tillable, cultivatable, sowing, harvesting and etc. This MTA feature was determined creation of digital control systems of two groups of automatic control and management of the basic energy and operational parameters: tractors, machines and vehicles as part of MTA. To the first group are appertained the automatic control system of tractor motor component loading, motion speed, frictional sliding. To the second group – automatic regulation system of operating depth, seed rate, treatment of liquid combined fertilizers and crop protection agents, filling and driving of various MTA. Novelty of researches consists in methodology of the organization of the centralized control and management of various technological processes at carrying out field works.


Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.


2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Oleksandr Kyriienko ◽  
Annie E. Paine ◽  
Vincent E. Elfving

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.


2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.


Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 446
Author(s):  
Alanoud Almutairi ◽  
Omar Bazighifan ◽  
Youssef N. Raffoul

The aim of this work is to investigate the oscillation of solutions of higher-order nonlinear differential equations with a middle term. By using the integral averaging technique, Riccati transformation technique and comparison technique, several oscillatory properties are presented that unify the results obtained in the literature. Some examples are presented to demonstrate the main results.


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