scholarly journals Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values

2018 ◽  
Vol 16 (1) ◽  
pp. 507-521 ◽  
Author(s):  
Petr Hasil ◽  
Michal Veselý
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Qualitative Theory ◽  
Linear Differential Equations ◽  
Power Functions ◽  
Mean Values ◽  
Linear Differential ◽  
Critical Oscillation ◽  
Non Linear Equations ◽  
Oscillation Constant

AbstractThe paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.

scholarly journals On non-homogeneous canonical third-order linear differential equations

1994 ◽  
Vol 57 (2) ◽  
pp. 138-148 ◽  
Author(s):  
N. Parhi
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.

scholarly journals On a class of non-linear differential equations with exact solution

2012 ◽  
Vol 34 (1) ◽  
pp. 7-17
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Solid Mechanics ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Second Order Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The present paper deals with a class of non-linear ordinary second-order differential equations with exact solutions. A procedure for finding the general exact solution based on a known particular one is derived. For illustration solutions of some non-linear equations occurred in many problems of solid mechanics are considered.

scholarly journals The differential equations of ballistics

1933 ◽  
Vol 231 (694-706) ◽  
pp. 263-288
Keyword(s):  
Differential Equations ◽  
Applied Mathematics ◽  
Linear Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Pressure Index ◽  
Internal Ballistics ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The differential equations arising in most branches of applied mathematics are linear equations of the second order. Internal ballistics, which is the dynamics of the motion of the shot in a gun, requires, except with the simplest assumptions, the discussion of non-linear differential equations of the first and second orders. The writer has shown in a previous paper* how such non-linear equations arise when the pressure-index a in the rate-of-burning equation differs from unity, although only the simplified case of non-resisted motion was there considered. It is proposed in the present investigation to examine some cases of resisted motion taking the pressure-index equal to unity, to give some extensions of the previous work, and to consider, so far as is possible, the nature and the solution of the types of differential equations which arise.

scholarly journals On the calculus of symbols.—Fourth memoir. With applications to the theory of non-linear differential equations

1864 ◽  
Vol 13 ◽  
pp. 423-432
Keyword(s):  
Differential Equations ◽  
Linear Function ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Linear Functions ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

In the preceding memoirs on the Calculus of Symbols, systems have been constructed for the multiplication and division of non-commutative symbols subject to certain laws of combination; and these systems suffice or linear differential equations. But when we enter upon the consideration of non-linear equations, we see at once that these methods do not apply. It becomes necessary to invent some fresh mode of calculation, and a new notation, in order to bring non-linear functions into a condition which admits of treatment by symbolical algebra. This is the object of the following memoir. Professor Boole has given, in his 'Treatise on Differential Equations,’ a method due to M. Sarrus, by which we ascertain whether a given non-linear function is a complete differential. This method, as will be seen by anyone who will refer to Professor Boole s treatise, is equivalent to finding the conditions that a non-linear function may be externally divisible by the symbol of differentiation. In the following paper I have given a notation by which I obtain the actual expressions for these conditions, and for the symbolical remainders arising in the course of the division, and have extended my investigations to ascertaining the results of the symbolical division of non-linear functions by linear functions of the symbol of differentiation. Let F ( x, y, y 1 , y 2 , y 3 . . . . y n ) be any non-linear function, in which y 1 , y 2 , y 3 . . . . y n denote respectively the first, second, third, . . . . n th differential of y with respect to ( x ).

scholarly journals Some solvable non-linear equations related to aerodynamic instability phenomena

1994 ◽  
Vol 16 (4) ◽  
pp. 11-14
Author(s):  
Nguyen Dang Bich ◽  
Nguyen Vo Thong
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Aerodynamic Forces ◽  
Non Linear ◽  
Aerodynamic Instability ◽  
Linear Differential ◽  
Non Linear Equations

This article proposes some forms of aerodynamic forces, looks for accurate solutions of core - pendent non-linear differential equations and analyses the characteristics of aerodynamic forces and of equation's solution. Found solutions proves that aerodynamic forces are formed from two elements: element of non-linear and dispersion, that single solutions are usually found and aerodynamic instability easy occurs.

scholarly journals Conditional Oscillation of Half-Linear Differential Equations with Coefficients Having Mean Values

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Petr Hasil ◽  
Robert Mařík ◽  
Michal Veselý
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Almost Periodic ◽  
Mean Values ◽  
Conditional Oscillation ◽  
The Mean ◽  
Linear Differential ◽  
Positive Coefficients ◽  
Oscillation Constant

We prove that the existence of the mean values of coefficients is sufficient for second-order half-linear Euler-type differential equations to be conditionally oscillatory. We explicitly find an oscillation constant even for the considered equations whose coefficients can change sign. Our results cover known results concerning periodic and almost periodic positive coefficients and extend them to larger classes of equations. We give examples and corollaries which illustrate cases that our results solve. We also mention an application of the presented results in the theory of partial differential equations.

scholarly journals A Dynamic Knowledge Model of Project Time-Cost Analysis Based on Trend Modelling

2019 ◽  
Vol 28 (1) ◽  
pp. 18-28
Author(s):  
Karel Doubravský ◽  
Radek Doskočil ◽  
Mirko Dohnal
Keyword(s):  
Project Management ◽  
Differential Equations ◽  
Cost Analysis ◽  
Trend Analysis ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Time Cost ◽  
Personnel Costs ◽  
Past Behavior ◽  
Linear Differential

This paper investigates the application of trend quantifiers of project time-cost analysis as a tool for decision-making support in the project management. Practical project management-related problems are solved under information shortages. It means that methods of statistical analysis cannot be easily used as they are based on the law of large numbers of observations. Numbers are information intensive quantifiers. The least information intensive quantifier is a trend; its values are increasing, constant, decreasing. If a derivative cannot be quantified by a trend, then nothing is known and therefore nothing can be analyzed/predicted. For this reason, the trend model M was created. The model M is based on a degraded set of differential equations or heuristics. A trend analysis of the model M is an evaluation of the relevant discrete set of solutions/scenarios S. A trend reconstruction is an evaluation of the model M if a (sub)set of scenarios S is given. The paper studies linear reconstruction, i.e. the model M is a set of linear differential equations. The trend reconstruction is partially reverse process to trend analysis. A case study has 7 variables (e.g. Project duration, Direct personnel costs, Indirect personal costs etc.) and the reconstructed set of linear differential equations has 7 equations. The set of 243 scenarios is obtained if this reconstructed set of trend linear equations is solved. Any future or past behavior of the model M can be described by a sequence of obtained scenarios.

scholarly journals A New Scheme Using Cubic B-Spline to Solve Non-Linear Differential Equations Arising in Visco-Elastic Flows and Hydrodynamic Stability Problems

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1078 ◽  
Author(s):  
Asifa Tassaddiq ◽  
Aasma Khalid ◽  
Muhammad Nawaz Naeem ◽  
Abdul Ghaffar ◽  
Faheem Khan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Main Idea ◽  
Linear Differential Equations ◽  
System Of Linear Equations ◽  
B Spline ◽  
Stability Problems ◽  
Non Linear ◽  
Linear Differential ◽  
Magnetic Stability

This study deals with the numerical solution of the non-linear differential equations (DEs) arising in the study of hydrodynamics and hydro-magnetic stability problems using a new cubic B-spline scheme (CBS). The main idea is that we have modified the boundary value problems (BVPs) to produce a new system of linear equations. The algorithm developed here is not only for the approximation solutions of the 10th order BVPs but also estimate from 1st derivative to 10th derivative of the exact solution as well. Some examples are illustrated to show the feasibility and competence of the proposed scheme.

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