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

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  • Li, Qiang
  • Li, Yongxiang

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.

Suggested Citation

  • Li, Qiang & Li, Yongxiang, 2015. "Monotone iterative technique for second order delayed periodic problem in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 654-664.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:654-664
    DOI: 10.1016/j.amc.2015.08.070
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    References listed on IDEAS

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    1. Yongxiang Li, 2012. "Positive Periodic Solutions of Second‐Order Differential Equations with Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    2. Qiang Li & Yongxiang Li, 2012. "On the Existence of Positive Periodic Solutions for Second‐Order Functional Differential Equations with Multiple Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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