Abstract and Applied Analysis

Global Positive Periodic Solutions of Generalized n -Species Competition Systems with Multiple Delays and Impulses

Zhenguo Luo and Liping Luo

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Abstract

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 = 1,2 , , n ;  x i ( t k + ) - x i ( t k - ) = θ i k x i ( t k ) ,  i = 1,2 , , 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 = 1,2 , , n ;  x i ( t k + ) - x i ( t k - ) = θ i k x i ( t k ) ,  i = 1,2 , , n ,  k Z + . It improves and generalizes a series of the well-known sufficiency theorems in the literature about the problems mentioned previously.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 980974, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450111

Digital Object Identifier
doi:10.1155/2013/980974

Mathematical Reviews number (MathSciNet)
MR3093763

Zentralblatt MATH identifier
1294.34078

Citation

Luo, Zhenguo; Luo, Liping. Global Positive Periodic Solutions of Generalized $n$ -Species Competition Systems with Multiple Delays and Impulses. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 980974, 12 pages. doi:10.1155/2013/980974. https://projecteuclid.org/euclid.aaa/1393450111


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