IJPAM: Volume 71, No. 4 (2011)

POSITIVE PERIODIC SOLUTIONS OF NEUTRAL
LOTKA-VOLTERRA COMPETITION
SYSTEMS ON TIME SCALES

Yan Lei$^1$, Yongkun Li$^2$
$^1$Department of Industry Cooperation
Kunming Metallurgy College
Kunming, Yunnan, 650033, P.R. CHINA
$^2$Department of Mathematics
Yunnan University
Kunming, Yunnan, 650091, P.R. CHINA


Abstract. By using a fixed point theorem of strict-set-contraction, some sufficient conditions are obtained for the existence of positive periodic solutions for a periodic neutral Lotka- Volterra competition system on time scales of the form
\begin{multline*} x_i^\Delta(t)=x_i(t)\bigg [r_i(t)- \sum\limits_{j=1}^na_{ij}... ...gma_{ij}(t,x_1(t),\ldots,x_n(t)))\bigg ],\quad i=1,2,\ldots,n, \end{multline*}
where $r_i,a_{ij},b_{ij},c_{ij}\in C(\mathbb{T},\mathbb{R}^+)(i,j=1,2,\ldots,n)$ are $\omega$-periodic functions, and $\tau_{ij},\sigma_{ij}\in C(\mathbb{T}\times\mathbb{R}^n,\mathbb{T})(i=1,2,\ldots,n)$ are $\omega$-periodic functions with respect to their first arguments, respectively.

Received: April 18, 2011

AMS Subject Classification: 34K13, 34K40, 34N05

Key Words and Phrases: positive periodic solution, neutral Lotka-Volterra system, time scales, strict-set-contraction

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 4