Positive periodic solutions of higher-order ordinary differential equations with delayed derivative terms
- ZHANG Huan, LI Yong-xiang
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(4):
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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.