Monotone iterative technique for nonlocal problems of damped elastic systems with delay

Abstract

In this paper, based on the monotone iterative technique and the operator semigroup theory, a class of nonlocal problem of structural damped elastic systems with delay is studied in the case of noncompact semigroups in ordered Banach space. First, on the premise of the existence of upper and lower mild solutions, the existence and uniqueness of mild solutions for the elastic system are obtained. Then, an existence theorem of positive mild solutions for elastic system is obtained without assuming lower and upper mild solutions. Finally, as the application of abstract results, the existence and uniqueness of mild solutions and positive mild solutions for two classes of nonlocal damped beam vibration equations with delay are discussed.

Keywords:

• Damped elastic systems with delay
• nonlocal problems
• monotone iterative technique
• $C_0$-semigroup
• fixed point theorem

2020 Mathematics Subject Classifications:

• 34G20
• 35L35
• 47D06
• 47H08
• 47J35

Acknowledgments

The authors are most grateful to the editor Professor and anonymous referees for the careful reading of the manuscript and valuable suggestions that helped in significantly improving an earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Consent for publication

All authors read and approved the final version of the manuscript.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 11661071, 12061062), Graduate Research Support project of Northwest Normal University (2021KYZZ01030).