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

Yongxiang Li; Ailan Liu

Mathematica Bohemica (2018)

  • Volume: 143, Issue: 1, page 11-24
  • ISSN: 0862-7959

Abstract

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This paper deals with the existence of positive ω -periodic solutions for the neutral functional differential equation with multiple delays ( u ( t ) - c u ( t - δ ) ) ' + a ( t ) u ( t ) = f ( t , u ( t - τ 1 ) , ⋯ , u ( t - τ 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 , ⋯ , x n ) . Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.

How to cite

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Li, Yongxiang, and Liu, Ailan. "Positive periodic solutions of a neutral functional differential equation with multiple delays." Mathematica Bohemica 143.1 (2018): 11-24. <http://eudml.org/doc/294331>.

@article{Li2018,
abstract = {This paper deals with the existence of positive $\omega $-periodic solutions for the neutral functional differential equation with multiple delays \[(u(t)-cu(t-\delta ))^\{\prime \}+a(t) u(t)=f(t, u(t-\tau \_1), \cdots , u(t-\tau \_n)).\] 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.},
author = {Li, Yongxiang, Liu, Ailan},
journal = {Mathematica Bohemica},
keywords = {neutral delay differential equation; positive periodic solution; cone; fixed point index},
language = {eng},
number = {1},
pages = {11-24},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive periodic solutions of a neutral functional differential equation with multiple delays},
url = {http://eudml.org/doc/294331},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Li, Yongxiang
AU - Liu, Ailan
TI - Positive periodic solutions of a neutral functional differential equation with multiple delays
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 1
SP - 11
EP - 24
AB - This paper deals with the existence of positive $\omega $-periodic solutions for the neutral functional differential equation with multiple delays \[(u(t)-cu(t-\delta ))^{\prime }+a(t) u(t)=f(t, u(t-\tau _1), \cdots , u(t-\tau _n)).\] 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.
LA - eng
KW - neutral delay differential equation; positive periodic solution; cone; fixed point index
UR - http://eudml.org/doc/294331
ER -

References

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