Monotone iterative technique for delay elastic systems in ordered Banach space

Abstract

We research extremal S-asymptotically ω-periodic mild solutions to elastic systems by using upper and lower solutions. In our first result, it is assumed that the semigroup is compact. In addition, in our second result, the semigroup does not need to be compact and not assuming lower and upper solutions. Our conclusion is drawn using measures of noncompactness. Finally, the existence of mild solutions for damped equations is discussed as an application.

Keywords:

• Damped elastic systems
• monotone iterative technique
• periodic mild solutions

Mathematics Subject Classifications:

• 34G20
• 34K30
• 34K37

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 11661071 and 12061062], Science Research Project for Colleges and Universities of Gansu Province [grant number 2022A-010], Lanzhou Youth Science and Technology Talent Innovation Project [grant number 2023-QN-106] and Project of NWNU-LKQN2023-02.