On the evolution differential inclusions under a noncompact evolution system

Volume 9, Issue 3, pp 1008--1018 http://dx.doi.org/10.22436/jnsa.009.03.29

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Authors

Min Wang - Library, Huaiyin Institute of Technology, Huaian 223003, P. R. China. Shaochun Ji - Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, P. R. China. Shu Wen - Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, P. R. China.

Abstract

We study the existence of mild solutions to differential inclusions with nonlocal conditions. The first result is established when evolution system is equicontinuous and multifunction is upper semi-continuous. Then another result is obtained when evolution system is not equicontinuous and not compact. The measure of noncompactness and the fixed point theorem for multivalued mappings play key roles in the proof. An example is provided to illustrate our results.

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Keywords

• nonlocal conditions
• measure of noncompactness
• Differential inclusions
• fixed point theorems
• mild solutions.

MSC

•  34G10
•  34A60

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