Positive periodic solutions of neutral logistic equations with distributed delays

Li Yongkun; Wang Guoqiao; Wang Huimei

Positive periodic solutions of neutral logistic equations with distributed delays

Li Yongkun
, Wang Guoqiao
, Wang Huimei

Research output: Contribution to journal › Article › peer-review

Abstract

Using a fixed point theorem of strict-set-contraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x′(t) = x(t)[a(t)-∑_i=1ⁿa_i(t)∫ _-Ti⁰x(t+θ)dμ_i(θ)-∑ _j=1^mb_j(t)∫_-T̂j ⁰x′(t+θ)dv_j(θ), where the coefficients a, a_i, b_j are continuous and periodic functions, with the same period. The values T_i,T̂_j are positive, and the functions μ_i,v_j are nondecreasing with ∫_-Ti⁰ dμ_i = 1 and ∫ _-Ti⁰dv_j = 1.

Original language	English
Pages (from-to)	1-10
Number of pages	10
Journal	Electronic Journal of Differential Equations
Volume	2007
State	Published - Aug 1 2007

Keywords

Neutral delay logistic equation
Positive periodic solution
Strict-set-contraction

Cite this

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title = "Positive periodic solutions of neutral logistic equations with distributed delays",

abstract = "Using a fixed point theorem of strict-set-contraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x′(t) = x(t)[a(t)-∑i=1nai(t)∫ -Ti0x(t+θ)dμi(θ)-∑ j=1mbj(t)∫-{\^T}j 0x′(t+θ)dvj(θ), where the coefficients a, ai, bj are continuous and periodic functions, with the same period. The values Ti,{\^T}j are positive, and the functions μi,vj are nondecreasing with ∫-Ti0 dμi = 1 and ∫ -Ti0dvj = 1.",

keywords = "Neutral delay logistic equation, Positive periodic solution, Strict-set-contraction",

author = "Li Yongkun and Wang Guoqiao and Wang Huimei",

year = "2007",

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day = "1",

language = "English",

volume = "2007",

pages = "1--10",

journal = "Electronic Journal of Differential Equations",

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TY - JOUR

T1 - Positive periodic solutions of neutral logistic equations with distributed delays

AU - Yongkun, Li

AU - Guoqiao, Wang

AU - Huimei, Wang

PY - 2007/8/1

Y1 - 2007/8/1

N2 - Using a fixed point theorem of strict-set-contraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x′(t) = x(t)[a(t)-∑i=1nai(t)∫ -Ti0x(t+θ)dμi(θ)-∑ j=1mbj(t)∫-T̂j 0x′(t+θ)dvj(θ), where the coefficients a, ai, bj are continuous and periodic functions, with the same period. The values Ti,T̂j are positive, and the functions μi,vj are nondecreasing with ∫-Ti0 dμi = 1 and ∫ -Ti0dvj = 1.

AB - Using a fixed point theorem of strict-set-contraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x′(t) = x(t)[a(t)-∑i=1nai(t)∫ -Ti0x(t+θ)dμi(θ)-∑ j=1mbj(t)∫-T̂j 0x′(t+θ)dvj(θ), where the coefficients a, ai, bj are continuous and periodic functions, with the same period. The values Ti,T̂j are positive, and the functions μi,vj are nondecreasing with ∫-Ti0 dμi = 1 and ∫ -Ti0dvj = 1.

KW - Neutral delay logistic equation

KW - Positive periodic solution

KW - Strict-set-contraction

UR - https://www.scopus.com/pages/publications/33846220681

M3 - Article

AN - SCOPUS:33846220681

SN - 1072-6691

VL - 2007

SP - 1

EP - 10

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

Positive periodic solutions of neutral logistic equations with distributed delays

Abstract

Keywords

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