Results on controllability and well-posedness of functional abstract second-order differential equations with state-dependent delay

Abstract

The major goal of this study is to demonstrate the existence and controllability of a second-order abstract differential system with state-dependent delay. We also discuss the well-posedness of the problem at hand. Finally, some examples are provided for the illustration of the main results.

Keywords:

• Abstract differential equation
• cosine families
• state-dependent delay
• well-posedness
• controllability

Mathematics Subject Classifications:

• Primary: 34K43
• Secondary: 93C10
• 93C55

Acknowledgments

The authors express their gratitude to the anonymous referees for their helpful suggestions and corrections.

Availability of data and materials

No data were used to support this work.

Disclosure statement

The authors declare that they have no competing interests.

Authors' contributions

All authors contributed equally in writing this article. All authors read and approved the final manuscript.

Additional information

Funding

This research did not receive any external funding.