The initial value problems of first order impulsive differential equations in Banach spaces

2000 ◽  
Vol 21 (1) ◽  
pp. 33-42
Author(s):  
Sun Qinfu ◽  
Luan Shixia
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Initial Value Problems ◽  
Impulsive Differential Equations ◽  
Initial Value ◽  
First Order

scholarly journals Nonlinear impulsive Volterra integral equations in Banach spaces and applications

1993 ◽  
Vol 6 (1) ◽  
pp. 35-48 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Integral Equations ◽  
Initial Value Problems ◽  
Infinite System ◽  
Impulsive Differential Equations ◽  
Volterra Integral Equations ◽  
Initial Value ◽  
First Order ◽  
Maximal Solutions

In this paper, we first extend results on the existence of maximal solutions for nonlinear Volterra integral equations in Banach spaces to impulsive Volterra integral equations. Then, we give some applications to initial value problems for first order impulsive differential equations in Banach spaces. The results are demonstrated by means of an example of an infinite system for impulsive differential equations.

scholarly journals Initial value problems for integro-differential equations of Volterra type in Banach spaces

1994 ◽  
Vol 7 (1) ◽  
pp. 13-23 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Initial Value Problems ◽  
Extremal Solutions ◽  
Comparison Result ◽  
Initial Value ◽  
Volterra Type ◽  
First Order

This paper investigates the extremal solutions of initial value problems for first order integro-differential equations of Volterra type in Banach spaces by means of establishing a comparison result.

scholarly journals Initial value problems for first order impulsive integro-differential equations of Volterra type in Banach spaces

2007 ◽  
Vol 5 (1) ◽  
pp. 9-26 ◽  
Author(s):  
Jiang Zhu ◽  
Yajuan Yu ◽  
Vasile Postolica
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Initial Value Problems ◽  
Finite Interval ◽  
Estimation Method ◽  
Partial Ordering ◽  
Initial Value ◽  
Volterra Type ◽  
First Order ◽  
Noncompactness Measure

In this paper, we use a new method and combining the partial ordering method to study the existence of the solutions for the first order nonlinear impulsive integro-differential equations of Volterra type on finite interval in Banach spaces and for the first order nonlinear impulsive integro-differential equations of Volterra type on infinite interval with infinite number impulsive times in Banach spaces. By introducing an interim space and using progressive estimation method, some restrictive conditions on impulsive terms, used before, such as, prior estimation, noncompactness measure estimations are deleted.

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