scholarly journals Some Important Criteria for Oscillation of Non-Linear Differential Equations with Middle Term

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 346 ◽  
Author(s):  
Saad Althobati ◽  
Omar Bazighifan ◽  
Mehmet Yavuz
Keyword(s):  
Differential Equations ◽  
Comparison Method ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Middle Term ◽  
Oscillation Criteria ◽  
First Order ◽  
Non Linear ◽  
Linear Differential ◽  
Higher Order Differential Equations

In this work, we present new oscillation conditions for the oscillation of the higher-order differential equations with the middle term. We obtain some oscillation criteria by a comparison method with first-order equations. The obtained results extend and simplify known conditions in the literature. Furthermore, examining the validity of the proposed criteria is demonstrated via particular examples.

On reducible non-linear differential equations occurring in mechanics

1953 ◽  
Vol 217 (1130) ◽  
pp. 327-343 ◽  
Keyword(s):  
Differential Equations ◽  
Basic Problem ◽  
Order Differential Equation ◽  
Linear Differential Equations ◽  
Qualitative Information ◽  
First Order ◽  
Internal Ballistics ◽  
Integral Curves ◽  
Non Linear ◽  
Linear Differential

The purpose of this paper is to present a new method of approach to certain problems in mechanics which give rise to ordinary non-linear differential equations of the second order. The method, which is based on the topology of the integral curves of a first-order differential equation, aims at providing qualitative information which can be used, if necessary, in guiding numerical calculations of the solutions. Among the equations discussed are those of Emden and Blasius, which occur in astrophysics and in boundary-layer theory respectively; these, together with the equation of a basic problem of internal ballistics, are shown to be reducible to different forms of the same first-order equation, which is itself of a type studied originally by Poincaré in another connexion.

Generalized systems of linear differential equations

1981 ◽  
Vol 89 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
Rainer Pfaff
Keyword(s):  
Differential Equations ◽  
Bounded Variation ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Generalized Systems ◽  
Linear Differential ◽  
Derivatives Of

SynopsisWe consider ordinary linear differential systems of first order with distributional coefficients and distributional nonhomogeneous terms. Firstly the coefficients are assumed to be functions, secondly to be first order distributions (i.e. first derivatives of functions which are integrable or of bounded variation), and thirdly to be distributions of higher order.

On The Motion of Three Vortices

1949 ◽  
Vol 1 (3) ◽  
pp. 257-270 ◽  
Author(s):  
J. L. Synge
Keyword(s):  
Differential Equations ◽  
Incompressible Fluid ◽  
Linear Differential Equations ◽  
Vortex Filaments ◽  
First Order ◽  
Perfect Incompressible Fluid ◽  
Non Linear ◽  
The Mean ◽  
Linear Differential

In a perfect incompressible fluid extending to infinity, the determination of the motion of N parallel rectilinear vortex filaments involves the solution of N non-linear differential equations, each of the first order. The method of Kirchhoff provides certain constants of the motion. If we describe the positions of the vortices by their point-traces on a plane perpendicular to them, the following facts follow from the theory of Kirchhoff:(1.1) The mean centre of the system is fixed.

On Non-Linear Differential Equations of First Order

1950 ◽  
Vol 72 (2) ◽  
pp. 347
Author(s):  
Philip Hartman ◽  
Aurel Wintner
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
First Order ◽  
Non Linear ◽  
Linear Differential

scholarly journals Oscillation Results for Nonlinear Higher-Order Differential Equations with Delay Term

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 446
Author(s):  
Alanoud Almutairi ◽  
Omar Bazighifan ◽  
Youssef N. Raffoul
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Higher Order ◽  
Middle Term ◽  
Delay Term ◽  
Integral Averaging Technique ◽  
Equations With Delay ◽  
Oscillation Of Solutions ◽  
Comparison Technique ◽  
Higher Order Differential Equations

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.

Sign in / Sign up

Export Citation Format

Share Document