Monotone iterative technique for second order delayed periodic problem in Banach spaces

Qiang Li and Yongxiang Li

Applied Mathematics and Computation, 2015, vol. 270, issue C, 654-664

Abstract: In this paper, we deal with the existence of ω-periodic solutions for second-order functional differential equation with delay in E−u′′(t)=f(t,u(t),u(t−τ)),t∈R,where E is an ordered Banach space, f:R×E×E→E is a continuous function which is ω-periodic in t and τ ≥ 0 is a constant. We first build a new maximum principle for the ω-periodic solutions of the corresponding linear equation with delay. With the aid of this maximum principle, under the assumption that the nonlinear function is quasi-monotonicity, we study the existence of the minimal and maximal periodic solutions for abstract delayed equation by combining perturbation method and monotone iterative technique of the lower and upper solutions.

Keywords: Second-order differential equation; Delay; Periodic solution; Existence; Upper and lower solutions; Monotone iterative technique (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:654-664

DOI: 10.1016/j.amc.2015.08.070

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