scholarly journals A unique solution of initial value problems for first order impulsive integro-differential equations of mixed type in Banach spaces

2002 ◽  
Vol 275 (1) ◽  
pp. 369-385 ◽  
Author(s):  
Li Shan Liu ◽  
Congxin Wu ◽  
Fei Guo
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Unique Solution ◽  
Initial Value Problems ◽  
Mixed Type ◽  
Initial Value ◽  
First Order ◽  
Equations Of Mixed Type

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 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.

scholarly journals Numerical solutions of nonstandard first order initial value problems

1992 ◽  
Vol 5 (1) ◽  
pp. 69-82 ◽  
Author(s):  
M. Venkatesulu ◽  
P. D. N. Srinivasu
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Unique Solution ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Initial Value ◽  
First Order ◽  
Physical Phenomena

Differential equations of the form y′=f(t,y,y′), where f is not necessarily linear in its arguments, represent certain physical phenomena and are known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier, we established the existence of a (unique) solution of the nonstandard initial value problem (NSTD IV P) y′=f(t,y,y′), y(t0)=y0 under certain natural hypotheses on f. In this paper we present some first order convergent numerical methods for finding the approximate solutions of the NST D I V Ps.

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.

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