A class of nonlinear integrodifferential impulsive periodic systems of mixed type and optimal controls on Banach space

2009 ◽  
Vol 34 (1-2) ◽  
pp. 465-484 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei
Keyword(s):  
Banach Space ◽  
Mixed Type ◽  
Periodic Systems ◽  
Optimal Controls

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 Terminal value problems of impulsive integro-differential equations in Banach spaces

1997 ◽  
Vol 10 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Banach Spaces ◽  
Mixed Type ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
First Order ◽  
Monotone Iterative ◽  
Equations Of Mixed Type ◽  
Nonnegative Solutions

This paper uses cone theory and the monotone iterative technique to investigate the existence of minimal nonnegative solutions of terminal value problems for first order nonlinear impulsive integro-differential equations of mixed type in a Banach space.

scholarly journals Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Aneta Sikorska-Nowak ◽  
Grzegorz Nowak
Keyword(s):  
Banach Space ◽  
Integrodifferential Equation ◽  
Mixed Type ◽  
Measure Of Noncompactness ◽  
Existence Theorems ◽  
Continuous Functions ◽  
Measure Of Weak Noncompactness ◽  
Equations Of Mixed Type ◽  
Weakly Sequentially Continuous ◽  
Equation Of Mixed Type

We prove two existence theorems for the integrodifferential equation of mixed type:x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds),x(0)=x0, where in the first part of this paperf, g, h, xare functions with values in a Banach spaceEand integrals are taken in the sense of Henstock-Kurzweil (HK). In the second partf, g, h, xare weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functionsf, g, h, xsatisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.

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.

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