Controllability for a class of integro-differential evolution equations involving non-local initial conditions

ABSTRACT

This paper deals with the exact controllability for a class of first-order integro-differential evolution equations involving non-local initial conditions. By using Sadovskii fixed point theorem, exact controllability results are obtained without assuming the compactness and Lipschitz conditions for non-local functions. An example is given to illustrate the effectiveness of the abstract results.

KEYWORDS:

• Non-local evolution equation
• exact controllability
• the measure of non-compactness
• fixed point theorem

MATHEMATICS SUBJECT CLASSIFICATION(2010):

• 34G20
• 47H10
• 49J20

Acknowledgments

The authors wish to thank the referees for their helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is partially supported by NSF of Gansu Province [grant number 1308RJZA217].