scholarly journals Existence of periodic solutions for first-order evolution equations without coercivity

2003 ◽  
Vol 282 (2) ◽  
pp. 801-815 ◽  
Author(s):  
Yu-Qing Chen ◽  
Jong-Kyu Kim
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
First Order ◽  
Existence Of Periodic Solutions

scholarly journals The Integrability and Existence of Periodic Solutions on a First-Order Nonlinear Differential Equation with a Polynomial Nonlinear Term

2012 ◽  
Vol 2012 ◽  
pp. 1-26
Author(s):  
Ni Hua ◽  
Tian Li-Xin
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Nonlinear Differential Equation ◽  
Nonlinear Term ◽  
Order Differential Equation ◽  
First Order ◽  
Order Nonlinear Differential Equation ◽  
Existence Of Periodic Solutions ◽  
The Stability

This paper deals with a first-order differential equation with a polynomial nonlinear term. The integrability and existence of periodic solutions of the equation are obtained, and the stability of periodic solutions of the equation is derived.

Periodic solutions of ordinary differential equations with one-sided growth restrictions

1978 ◽  
Vol 82 (1-2) ◽  
pp. 95-106 ◽  
Author(s):  
J. Mawhin ◽  
W. Walter
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
First Order ◽  
Asymptotic Nature ◽  
Special Cases ◽  
Existence Of Periodic Solutions ◽  
Growth Restrictions ◽  
Functional Differential ◽  
The Right

SynopsisThe existence of periodic solutions is proved for first order vector ordinary and functional differential equations when the right-hand side satisfies a one-sided growth restriction of Wintner type together with some conditions of asymptotic nature. Special cases in the line of Landesman-Lazer and of Winston are explicited.

scholarly journals Hopf bifurcation at infinity with discontinuous nonlinearities

1991 ◽  
Vol 33 (2) ◽  
pp. 133-148 ◽  
Author(s):  
Xiangjian He
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Imaginary Axis ◽  
Linear Part ◽  
Order System ◽  
Bifurcation Problem ◽  
System Of Integral Equations ◽  
First Order ◽  
Discontinuous Nonlinearities ◽  
Existence Of Periodic Solutions

AbstractIn this paper, we consider the existence of a family of periodic solutions of large amplitude when a pair of eigenvalues of the linear part of a first-order system of ordinary differential equations crosses the imaginary axis. We refer to this problem as a Hopf bifurcation problem at infinity. In our work, the nonlinearities may be discontinuous at the origin, and the proof of existence of periodic solutions is arrived at through the corresponding system of integral equations. The applicability of the result is demonstrated by the study of the dynamics of a train truck wheelset system.

scholarly journals Global exponential stability and existence of periodic solutions of fuzzy wave equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Wei Liu ◽  
Yimin Lou
Keyword(s):  
Periodic Solution ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
First Order ◽  
Variable Substitution ◽  
Existence Of Periodic Solutions

AbstractIn this paper, the global exponential stability and the existence of periodic solutions of fuzzy wave equations are investigated. By variable substitution the system of partial differential equations (PDEs) is transformed from second order to first order. Some sufficient conditions that ensure the global exponential stability and the existence of periodic solution of the system are obtained by an analysis that uses a suitable Lyapunov functional. In addition, a concrete example is given to show the effectiveness of the results.

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