Semigroups and Asymptotic Stability of Nonlinear Differential Equations

1972 ◽  
Vol 3 (2) ◽  
pp. 371-379 ◽  
Author(s):  
C. V. Pao
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Nonlinear Differential Equations

Nonlinear Differential Equations and Feedback Control Design for the Urban–Rural Resident Pension Insurance in China

2015 ◽  
Vol 25 (14) ◽  
pp. 1540029
Author(s):  
Lijian Wang
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Control Design ◽  
Rural Resident ◽  
Pension Insurance ◽  
Modern Control Theory ◽  
Insurance System ◽  
Urban Rural ◽  
Pension Insurance System

Facing many problems of the urban–rural resident pension insurance system in China, one should firstly make sure that this system can be optimized. This paper, based on the modern control theory, sets up differential equations as models to describe the urban–rural resident pension insurance system, and discusses the globally asymptotic stability in the sense of Liapunov for the urban–rural resident pension insurance system in the new equilibrium point. This research sets the stage for our further discussion, and it is theoretically important and convenient for optimizing the urban–rural resident pension insurance system.

scholarly journals On Stability of Certain Class of 3-Rd Order Nonlinear Control Systems

2014 ◽  
Vol 22 (35) ◽  
pp. 39-47
Author(s):  
Oleg Palumbíny ◽  
Martin Neštický
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Nonlinear Control ◽  
Control Systems ◽  
Nonlinear Differential Equations ◽  
Nonlinear Control Systems ◽  
Third Order

AbstractThe paper deals with a certain class of nonautonomous ordinary third-order nonlinear differential equations L3y=f(t,L0y,L1y,L2y) with quasi-derivatives. A criterion of asymptotic stability in Liapunov sense as well as a criterion of instability in Liapunov sense is derived. The results are illustrated by two examples.

scholarly journals Existence and Stability of Periodic Solution to Delayed Nonlinear Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xiang Gu ◽  
Huicheng Wang ◽  
P. J. Y. Wong ◽  
Yonghui Xia
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Lyapunov Functional ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Competition System ◽  
Existence And Stability

The main purpose of this paper is to study the periodicity and global asymptotic stability of a generalized Lotka-Volterra’s competition system with delays. Some sufficient conditions are established for the existence and stability of periodic solution of such nonlinear differential equations. The approaches are based on Mawhin’s coincidence degree theory, matrix spectral theory, and Lyapunov functional.

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