Mathematica Bohemica, online first, 14 pp.

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.

Yongxiang Li, Ailan Liu, Department of Mathematics, Northwest Normal University, 967 Anning East Road, Lanzhou 730070, People's Republic of China, e-mail:,

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

Classification (MSC 2010): 34K13, 34K40, 47H11

DOI: 10.21136/MB.2017.0050-16

Full text available as PDF.

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