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 Volume 10, Number 2, 2020, Pages 495-513 The method of lower and upper solutions for damped elastic systems in Banach spaces Haide Gou,Yongxiang Li Keywords:Damped elastic systems, extremal mild solution, the method of lower and upper solution, measure of noncompactness. Abstract: In this paper, we are concerned with the initial value problem of a class of damped elastic systems in an order Banach spaces $E$. By employing the method of lower and upper solutions, we discuss the existence of extremal mild solutions between lower and upper mild solutions for such problem with the associated semigroup is equicontinuous. In addition, two examples are given to illustrate our results. PDF      Download reader