Geodesic
Positive periodic solutions of a neutral functional differential equation with multiple delays
Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 11-24
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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.
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.
DOI : 10.21136/MB.2017.0050-16
Classification : 34K13, 34K40, 47H11
Keywords: neutral delay differential equation; positive periodic solution; cone; fixed point index 
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Li, Yongxiang; Liu, Ailan. Positive periodic solutions of a neutral functional differential equation with multiple delays. Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 11-24. doi: 10.21136/MB.2017.0050-16

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