JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (4): 29-36.doi: 10.6040/j.issn.1671-9352.0.2018.258

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Positive periodic solutions of higher-order ordinary differential equations with delayed derivative terms

ZHANG Huan, LI Yong-xiang*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-04-08

Abstract: This paper deals with the existence of positive ω-periodic solutions for the higher-order ordinary differential equation with delayed derivative terms in nonlinearityu(n)(t)+a(t)u(t)=f(t, u(t-τ0(t)), u'(t-τ1(t)),…, u(n-1)(t-τn-1(t))), t∈R,where n≥2, a:R→(0,∞)is a continuous function which is ω-periodic, f:R×[0,∞)×Rn-1→[0,∞)is a continuous function which is ω-periodic on t, and τk:R→[0,∞)is a continuous function which is ω-periodic, k=0,1,…,n-1. By using the perturbation method of positive operator and fixed point index theory in cones, we obtain the existence results of positive ω-periodic solutions for the equation.

Key words: differential equation with delay, positive periodic solution, cone, fixed point index

CLC Number: 

  • O175.15
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