Positive periodic solutions of a neutral functional differential equation with multiple delays
Yongxiang Li, Ailan Liu
Received April 11, 2016. First published May 18, 2017.
Abstract: This paper deals with the existence of positive $\omega$-periodic solutions for the neutral functional differential equation with multiple delays $(u(t)-cu(t-\delta))'+a(t) u(t)=f(t, u(t-\tau_1), \cdots, u(t-\tau_n))$. The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of $c$ and the coefficient function $a(t)$, and the nonlinearity $f(t, x_1,\cdots, x_n)$. Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.
Keywords: neutral delay differential equation; positive periodic solution; cone; fixed point index
Affiliations: Yongxiang Li, Ailan Liu, Department of Mathematics, Northwest Normal University, 967 Anning East Road, Lanzhou 730070, People's Republic of China, e-mail: email@example.com, firstname.lastname@example.org