Resumen de Positive Mild Solutions for Damped Elastic Systems with Delay and Nonlocal Conditions in Ordered Banach Space

Mei Wei, Yongxiang Li, Qiang Li

• In this paper, the existence of minimal positive mild solution of a class of structural damped elastic systems with delay and nonlocal conditions on infinite interval are established in ordered Banach spaces. Without assuming the existence of upper and lower solutions of the equation, the conclusions are obtained directly from the characteristics of C0−semigroup T (t)(t ≥ 0) by using monotone iterative technique and fixed point theorem. At the end, the nonlocal problem of the vibration equation of a concrete simply supported beam is taken as an example to illustrate the feasibility and practical application value of our abstract results.