scholarly journals Periodic solutions of a class of integrodifferential impulsive periodic systems with time-varying generating operators on Banach space

2009 ◽  
pp. 1-17 ◽  
Author(s):  
Jinrong Wang ◽  
Xiaoling Xiang ◽  
Wei Wei
Keyword(s):  
Banach Space ◽  
Periodic Solutions ◽  
Periodic Systems ◽  
Time Varying ◽  
Generating Operators

scholarly journals Periodic Solutions of Semilinear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Mixed Type ◽  
Evolution Operator ◽  
Mild Solutions ◽  
Integral Operators ◽  
Periodic Systems ◽  
Time Varying ◽  
Type Integral ◽  
Generating Operators

A class of semilinear impulsive periodic systems with time-varying generating operators on Banach space is considered. Using impulsive periodic evolution operator given by us, theT0-periodicPC-mild solution is introduced and suitablePoincaréoperator is constructed. Showing the compactness ofPoincaréoperator and using a new generalized Gronwall inequality with mixed type integral operators given by us, we utilize Leray-Schauder fixed point theorem to prove the existence ofT0-periodicPC-mild solutions. Our method is an innovation and it is much different from methods of other papers. At last, an example is given for demonstration.

Further Remarks on the Existence of Periodic Solutions of Linear Time Varying Periodic Fractional Order Systems

2017 ◽  
Author(s):  
XueFeng Zhang ◽  
YangQuan Chen
Keyword(s):  
Laplace Transform ◽  
Periodic Solutions ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Linear Time ◽  
Periodic Systems ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Order Linear ◽  
Existence Of Periodic Solutions

Existence of periodic solutions of fractional order dynamic systems is an important and difficult issue in fractional order systems field. In this paper, the non existence of completely periodic solutions and existence of partly periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic systems are discussed. A new property of Laplace transform of periodic function is derived. The non existences of completely periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic fractional order systems are presented by Laplace transform method and contradiction approach. The existence of partly periodic solutions of fractional order dynamic systems are proved by constructing numerical examples and considering Laplace transform property approaches. The examples and state figures are given to illustrate the effectiveness of conclusion presented.

scholarly journals Existence of Periodic Solutions for Integrodifferential Impulsive Periodic System on Banach Space

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Periodic System ◽  
Evolution Operator ◽  
Mild Solutions ◽  
Periodic Systems ◽  
Gronwall Lemma ◽  
Existence Of Periodic Solutions

This paper deals with a class of integrodifferential impulsive periodic systems on Banach space. Using impulsive periodic evolution operator given by us, theT0-periodicPC-mild solution is introduced and suitablePoincaréoperator is constructed. By virtue of the generalized new Gronwall lemma with impulse andB-norm, the estimate on thePC-mild solutions is derived. Showing the continuity and compactness of thePoincaréoperator, we utilize Horn's fixed point theorem to prove the existence ofT0-periodicPC-mild solutions when thePC-mild solutions are bounded and ultimate bounded. This extends the study of periodic solutions of integrodifferential periodic system without impulse to integrodifferential periodic system with impulse on general Banach spaces. At last, an example is given for demonstration.

scholarly journals On the equivalence of three-dimensional differential systems

2020 ◽  
Vol 18 (1) ◽  
pp. 1164-1172
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Systems ◽  
Structural Form ◽  
Differential Systems

Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

On the Stability Properties of a Periodically Forced, Time-Varying Mass System

2009 ◽  
Author(s):  
W. T. van Horssen ◽  
O. V. Pischanskyy ◽  
J. L. A. Dubbeldam
Keyword(s):  
Periodic Solutions ◽  
Forced Vibrations ◽  
Time Varying ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Stability Properties ◽  
Single Degree ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Varying Mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.

Existence of Affine-Periodic Solutions to Newton Affine-Periodic Systems

2018 ◽  
Vol 25 (3) ◽  
pp. 437-455 ◽  
Author(s):  
Fei Xu ◽  
Xue Yang ◽  
Yong Li ◽  
Moxin Liu
Keyword(s):  
Periodic Solutions ◽  
Periodic Systems
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