Abstract
The goal of this paper is to consider damped elastic systems with delay and nonlocal conditions in the framework of ordered Banach spaces. Firstly, we investigate the existence of minimal positive S-asymptotically ω-periodic mild solution for structural damped elastic systems with delay and nonlocal conditions on infinite interval. Secondly, based on monotone iterative technique coupled with fixed point theorem, the existence of minimal positive S-asymptotically ω-periodic mild solution is discussed without assuming the existence of upper and lower solutions. Finally, a concrete problem regarding the vibration equation of simply supported beam is given to illustrate the feasibility of our abstract results.
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