Qualitative Behavior of the Solutions of Periodic First Order Scalar Differential Equations with Strictly Convex Coercive Nonlinearity

In continuous applications in electrodynamics, neural networks, quantum mechanics, electromagnetism, and the field of time symmetric, fluid dynamics, neutral differential equations appear when modeling many problems and phenomena. Therefore, it is interesting to study the qualitative behavior of solutions of such equations. In this study, we obtained some new sufficient conditions for oscillations to the solutions of a second-order delay differential equations with sub-linear neutral terms. The results obtained improve and complement the relevant results in the literature. Finally, we show an example to validate the main results, and an open problem is included.

Download Full-text

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

Asymptotic Analysis ◽

10.3233/asy-211710 ◽

2021 ◽

pp. 1-19

Author(s):

Calogero Vetro ◽

Dariusz Wardowski

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Order Differential Equation ◽

Nonlinear Differential Equations ◽

Oscillatory Behavior ◽

Third Order ◽

First Order ◽

Third Order Differential Equation ◽

Comparison Technique ◽

First Order Differential Equations

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.

Download Full-text

New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

Symmetry ◽

10.3390/sym13060934 ◽

2021 ◽

Vol 13 (6) ◽

pp. 934

Author(s):

Shyam Sundar Santra ◽

Khaled Mohamed Khedher ◽

Kamsing Nonlaopon ◽

Hijaz Ahmad

Keyword(s):

Asymptotic Behavior ◽

Differential Equations ◽

Sufficient Conditions ◽

Impulsive Differential Equations ◽

Oscillatory Behavior ◽

Second Order ◽

Discrete Equation ◽

Qualitative Behavior ◽

Differential Systems ◽

Impulsive Differential Systems

The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges to zero asymptotically), then the discrete equation of similar type do not disturb the oscillatory or asymptotic behavior of the impulsive system, when impulse satisfies the discrete equation. Further, some illustrative examples showing applicability of the new results are included.

Download Full-text

On the Strong Stability of First-Order Operator-Differential Equations

Differential Equations ◽

10.1023/b:dieq.0000043528.60501.e9 ◽

2004 ◽

Vol 40 (5) ◽

pp. 703-710 ◽

Cited By ~ 1

Author(s):

D. R. Bojovic ◽

B. S. Jovanovic ◽

P. P. Matus

Keyword(s):

Differential Equations ◽

Strong Stability ◽

Order Operator ◽

First Order

Download Full-text

First-Order Differential Equations

Differential Equations ◽

10.1007/978-3-030-20506-5_2 ◽

2019 ◽

pp. 105-153

Author(s):

Allan Struthers ◽

Merle Potter

Keyword(s):

Differential Equations ◽

First Order ◽

First Order Differential Equations

Download Full-text

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-1990-11-1201 ◽

1990 ◽

Vol 45 (11-12) ◽

pp. 1219-1229 ◽

Cited By ~ 1

Author(s):

D.-A. Becker ◽

E. W. Richter

Keyword(s):

Differential Equations ◽

Linear Equations ◽

Mhd Equations ◽

Two Dimensional ◽

Invariant Solutions ◽

First Order ◽

Partially Invariant Solutions ◽

Quasilinear Systems ◽

Ideal Mhd ◽

Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

Download Full-text