Positive periodic solutions of a neutral functional differential equation with multiple delays

Abstract

This paper deals with the existence of positive $ømega$-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