In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2013 ( 2013), p. 1-12
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.
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2013
detail.hit.zdb_id:
2064801-7
SSG:
17,1
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