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.

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 Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Shayma Adil Murad ◽  
Hussein Jebrail Zekri ◽  
Samir Hadid
Keyword(s):  
Banach Space ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Existence And Uniqueness Theorem ◽  
Integral Boundary ◽  
Fredholm Type ◽  
Type Integral

We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.

scholarly journals On solutions of semilinear evolution integrodifferential equations with nonlocal conditions

2009 ◽  
Vol 40 (3) ◽  
pp. 257-269 ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Contraction Principle ◽  
Theory Of Evolution ◽  
Banach’S Contraction Principle

In this paper, by using the theory of evolution families, Banach's contraction principle and Schauder's fixed point theorem, we prove the existence of mild solutions of a class of semilinear evolution integrodifferential equations with nonlocal conditions in Banach space. An example is provided to illustrate the obtained results.

scholarly journals Existence of Mild Solutions for the Elastic Systems with Structural Damping in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hongxia Fan ◽  
Yongxiang Li ◽  
Pengyu Chen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Elastic System ◽  
Mild Solutions ◽  
Structural Damping ◽  
Initial Value ◽  
Operator Semigroups ◽  
Elastic Systems ◽  
Theoretical Results

This paper deals with the existence and uniqueness of mild solutions for a second order evolution equation initial value problem in a Banach space, which can model an elastic system with structural damping. The discussion is based on the operator semigroups theory and fixed point theorem. In addition, an example is presented to illustrate our theoretical results.

scholarly journals Multi-valued mappings and fixed points II

2006 ◽  
Vol 37 (1) ◽  
pp. 27-46 ◽  
Author(s):  
B. C. Dhage
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Mixed Type ◽  
Existence Results ◽  
Fixed Point Principles

In this paper, some hybrid fixed point principles for the sum of two multi-valued operators in a Banach space are proved and they are further applied to a certain integral inclu- sion of mixed type for proving the existence results under mixed Lipschitz and Carath´eodory conditions.

Sign in / Sign up

Export Citation Format

Share Document