Nonlinear impulsive integro-differential equations of mixed type and optimal controls

Abstract

In this article, nonlinear impulsive integro-differential equations of mixed type on Banach spaces are considered. Existence of PC-mild solutions is proved. Existence of optimal controls of systems governed by impulsive integro-differential equations of mixed type is also presented. An example is given for demonstration.

†Dedicated to Professor N.U. Ahmed on the occasion of his 70th birthday.

Keywords:

• Semigroup
• Integral operator of mixed type
• PWC-mild solution
• Compactness
• Existence

Keywords:

• Mathematics Subject Classifications 2000: 34G20
• 34K30
• 35B62
• 93C25

Acknowledgment

This work is supported by the National Science Foundation of China under Grant no. 10361002.

Notes

†Dedicated to Professor N.U. Ahmed on the occasion of his 70th birthday.