
Positive periodic solutions of higherorder ordinary differential equations with delayed derivative terms
 ZHANG Huan, LI Yongxiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(4):
2936.
doi:10.6040/j.issn.16719352.0.2018.258

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This paper deals with the existence of positive ωperiodic solutions for the higherorder ordinary differential equation with delayed derivative terms in nonlinearityu^{(n)}(t)+a(t)u(t)=f(t, u(tτ_{0}(t)), u'(tτ_{1}(t)),…, u^{(n1)}(tτ_{n1}(t))), t∈R,where n≥2, a:R→(0,∞)is a continuous function which is ωperiodic, f:R×［0,∞)×R^{n1}→［0,∞)is a continuous function which is ωperiodic on t, and τ_{k}:R→［0,∞)is a continuous function which is ωperiodic, k=0,1,…,n1. By using the perturbation method of positive operator and fixed point index theory in cones, we obtain the existence results of positive ωperiodic solutions for the equation.