Mild solutions of impulsive semilinear neutral evolution equations in Banach spaces

Volume 9, Issue 12, pp 6183--6194 http://dx.doi.org/10.22436/jnsa.009.12.23

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Authors

Xinan Hao - School of Statistics, Qufu Normal University, Qufu 273165, Shandong, P. R. China. - School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, P. R. China. Lishan Liu - School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, P. R. China. - Department of Mathematics and Statistics, Curtin University, WA6845, Perth, Australia. Yonghong Wu - Department of Mathematics and Statistics, Curtin University, WA6845, Perth, Australia.

Abstract

This paper is concerned with the existence of mild solutions for impulsive semilinear neutral functional integro-differential equations in Banach spaces. The existence result is obtained by using fractional power of operators, Mönch fixed point theorem, the piecewise estimation method and semigroup theory. Applications to partial differential systems are also given.

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Keywords

• Semilinear neutral evolution equations
• measure of non-compactness
• mild solution
• semigroup.

MSC

•  47D03
•  34K45
•  34K40

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