Qualitative theory of differential equations

1983 ◽  
pp. 302-321
Author(s):  
Martin Braun
Keyword(s):  
Differential Equations ◽  
Qualitative Theory

scholarly journals Nonuniform Continuity of the Osmosis K(2, 2) Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Aiyong Chen ◽  
Yong Ding ◽  
Wentao Huang
Keyword(s):  
Differential Equations ◽  
Small Amplitude ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Qualitative Theory ◽  
Travelling Wave Solutions ◽  
Solution Map ◽  
Wave Solutions ◽  
Periodic Travelling Wave ◽  
Uniformly Continuous

The qualitative theory of differential equations is applied to the osmosis K(2, 2) equation. The parametric conditions of existence of the smooth periodic travelling wave solutions are given. We show that the solution map is not uniformly continuous by using the theory of Himonas and Misiolek. The proof relies on a construction of smooth periodic travelling waves with small amplitude.

A weight-homogenous condition to the real Jacobian conjecture in

2021 ◽  
pp. 1-9
Author(s):  
Francisco Braun ◽  
Claudia Valls
Keyword(s):  
Differential Equations ◽  
Vector Fields ◽  
Qualitative Theory ◽  
Hamiltonian Vector ◽  
Jacobian Conjecture ◽  
Local Diffeomorphism ◽  
The Real ◽  
Hamiltonian Vector Fields ◽  
Real Linear

Abstract It is known that a polynomial local diffeomorphism $(f,\, g): {\mathbb {R}}^{2} \to {\mathbb {R}}^{2}$ is a global diffeomorphism provided the higher homogeneous terms of $f f_x+g g_x$ and $f f_y+g g_y$ do not have real linear factors in common. Here, we give a weight-homogeneous framework of this result. Our approach uses qualitative theory of differential equations. In our reasoning, we obtain a result on polynomial Hamiltonian vector fields in the plane, generalization of a known fact.

scholarly journals Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 218 ◽  
Author(s):  
Muhammad Sher ◽  
Kamal Shah ◽  
Michal Fečkan ◽  
Rahmat Ali Khan
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Topological Degree ◽  
Degree Theory ◽  
Qualitative Theory ◽  
Proportional Delay ◽  
Topological Degree Theory ◽  
Fractional Order Differential Equations ◽  
Delay Differential ◽  
Stability Results

With the help of the topological degree theory in this manuscript, we develop qualitative theory for a class of multi-terms fractional order differential equations (FODEs) with proportional delay using the Caputo derivative. In the same line, we will also study various forms of Ulam stability results. To clarify our theocratical analysis, we provide three different pertinent examples.

Qualitative Theory of Differential Equations

2006 ◽  
Author(s):  
Zhang Zhi-fen ◽  
Ding Tong-ren ◽  
Huang Wen-zao ◽  
Dong Zhen-xi
Keyword(s):  
Differential Equations ◽  
Qualitative Theory

scholarly journals Galoisian and qualitative approaches to linear Polyanin-Zaitsev vector fields

2018 ◽  
Vol 16 (1) ◽  
pp. 1204-1217
Author(s):  
Primitivo B. Acosta-Humánez ◽  
Alberto Reyes-Linero ◽  
Jorge Rodriguez-Contreras
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Vector Fields ◽  
Qualitative Theory ◽  
Parametric Family ◽  
Liénard Equation ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Qualitative Approaches ◽  
Lienard Equation

AbstractIn this paper we study a particular parametric family of differential equations, the so-called Linear Polyanin-Zaitsev Vector Field, which has been introduced in a general case in [1] as a correction of a family presented in [2]. Linear Polyanin-Zaitsev Vector Field is transformed into a Liénard equation and, in particular, we obtain the Van Der Pol equation. We present some algebraic and qualitative results to illustrate some interactions between algebra and the qualitative theory of differential equations in this parametric family.

scholarly journals Oscillation criteria for generalized Liénard type system

2018 ◽  
Vol 38 (1) ◽  
pp. 83-100
Author(s):  
Tohid Kasbi ◽  
Vahid Roomi ◽  
Aliasghar Jodayree Akbarfam
Keyword(s):  
Differential Equations ◽  
Type System ◽  
Qualitative Theory ◽  
Qualitative Behavior ◽  
Oscillation Criteria

‎In this work we use qualitative theory of differential equations to study the qualitative behavior of the solutions of a generalized Liénard‎‎ system‎. ‎Under quite general assumptions we present some sharp conditions under which the‎‎solutions of the system are oscillatory‎. ‎Some examples are presented to illustrate our results‎.

Differential Equations—Introduction and Qualitative Theory (Jane Cronin)

SIAM Review ◽  
1982 ◽  
Vol 24 (3) ◽  
pp. 358-360
Author(s):  
Theodore Laetsch
Keyword(s):  
Differential Equations ◽  
Qualitative Theory
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