Lower and upper solutions for damped elastic systems with delay in ordered Banach space.

In this paper, based on monotone iterative method in the presence of the lower and upper solutions, a class of nonlocal problem of structural damped elastic systems with delay are studied in the case of noncompact semigroups in ordered Banach space. Firstly, we introduce the concept of lower S-asymptotically ω -periodic solution and upper S-asymptotically ω -periodic solution, on the premise of the existence of upper and lower S-asymptotically ω -periodic solutions, the existence of maximal and minimal S-asymptotically ω -periodic 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 S-asymptotically ω -periodic solutions. Finally, as the application of abstract results, the existence and uniqueness of S-asymptotically ω -periodic mild solutions and positive mild solutions for a classes of nonlocal damped elastic systems with delay are discussed. [ABSTRACT FROM AUTHOR]