[Luo, Zhenguo] Natl Univ Def Technol, Dept Math, Changsha 410073, Hunan, Peoples R China.

[Luo, Liping; Luo, Zhenguo] Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.

[Luo, Zhenguo] N

Natl Univ Def Technol, Dept Math, Changsha 410073, Hunan, Peoples R China.

By applying the fixed point theorem in a cone of Banach space;we obtain an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of two kinds of generalized n -species competition systems with multiple delays and impulses as follows: x i ′ ( t ) = x i ( t ) [ a i ( t ) - b i ( t ) x i ( t ) - ∑ j = 1 n c i j ( t ) x i ( t - τ i j ( t ) ) - ∑ j = 1 n d i j ( t ) x j ( t - γ i j ( t ) ) - ∑ j = 1 n e i j ( t ) ∫ - σ i j 0 ‍ f i j ( s ) x j ( t + s ) d s ]; a . e .; t > 0;t ≠ t k; k ∈ Z +; i = 1;n; x i ( t k + ) - x i ( t k - ) = θ i k x i ( t k ); i = 1;n; k ∈ Z +;and x i ′ ( t ) = x i ( t ) [ a i ( t ) - b i ( t ) x i ( t ) + ∑ j = 1 n c i j ( t ) x i ( t - τ i j ( t ) ) - ∑ j = 1 n d i j ( t ) x j ( t - γ i j ( t ) ) - ∑ j = 1 n e i j ( t ) ∫ - σ i j 0 ‍ f i j ( s ) x j ( t + s ) d s ]; a . e .; t > 0; t ≠ t k; k ∈ Z +; i = 1;n; x i ( t k + ) - x i ( t k - ) = θ i k x i ( t k ); i = 1;n; k ∈ Z + . It improves and generalizes a series of the well-known sufficiency theorems in the literature about the problems mentioned previously. Published: 2013 First available in Project Euclid: 26 February 2014 zbMATH: 1294.34078 MathSciNet: MR3093763 Digital Object Identifier: 10.1155/2013/980974

数学与统计学院