Mild solution of semilinear impulsive integro-differential evolution equation in Banach spaces

Hao, X.; Liu, Lishan

doi:10.1002/mma.4350

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Authors

Hao, X.

Liu, Lishan

Date

2017

Type

Journal Article

Metadata

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Citation

Hao, X. and Liu, L. 2017. Mild solution of semilinear impulsive integro-differential evolution equation in Banach spaces. Mathematical Methods in the Applied Sciences. 40 (13): pp. 4832-4841.

Source Title

Mathematical Methods in the Applied Sciences

DOI

10.1002/mma.4350

ISSN

0170-4214

School

Department of Mathematics and Statistics

URI

http://hdl.handle.net/20.500.11937/62986

Collection

Curtin Research Publications

Abstract

Copyright Â© 2017 John Wiley & Sons, Ltd. Through solving the problem step by step and by applying the method of a C 0 semigroup of operators combined with the Banach contraction theorem, we investigate the existence and uniqueness of a mild solution of semilinear impulsive integro-differential evolution equation in Banach spaces. In addition, an explicit iterative approximation sequence of the mild solution is derived. The assumed conditions in the present theorems are weaker and more general, and the results obtained are the generalizations and improvements of some known results. Examples are also given to illustrate our main results. Copyright Â© 2017 John Wiley & Sons, Ltd.