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2013 Global Positive Periodic Solutions of Generalized n -Species Competition Systems with Multiple Delays and Impulses
Zhenguo Luo, Liping Luo
Abstr. Appl. Anal. 2013(SI61): 1-12 (2013). DOI: 10.1155/2013/980974

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.

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Zhenguo Luo. Liping Luo. "Global Positive Periodic Solutions of Generalized n -Species Competition Systems with Multiple Delays and Impulses." Abstr. Appl. Anal. 2013 (SI61) 1 - 12, 2013. https://doi.org/10.1155/2013/980974

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1294.34078
MathSciNet: MR3093763
Digital Object Identifier: 10.1155/2013/980974

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI61 • 2013
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