具Gilpin-Ayala模型的正解唯一性與周期吸引性

張俊杰, 馬滿軍

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具Gilpin-Ayala模型的正解唯一性與周期吸引性

張俊杰1, 馬滿軍2

(1 南華大學(xué) 數(shù)理學(xué)院, 湖南 衡陽(yáng), 421001; 2 中國(guó)計(jì)量學(xué)院 理學(xué)院, 浙江 杭州, 310018)

利用上下解原理、最大值原理及分析技巧, 研究了一類具有驅(qū)動(dòng)擴(kuò)散的Gilpin-Ayala模型, 獲得該模型正解的存在唯一性, 以及周期吸引性的充分條件.

上下解原理; 最大值原理; 一致橢圓性

本文考慮具Gilpin-Ayala模型如下:

1 定義與引理

為了構(gòu)造式(2)的上下解序列, 引出定義2.

在上述有關(guān)假設(shè)和定義基礎(chǔ)下, 由文獻(xiàn)[1]中偏微分理論知識(shí)可得引理1-3.

以及初值條件:

關(guān)于引理4的一般證明過(guò)程可參看文獻(xiàn)[2]中定理3.2, 這里不再證明.

2 主要結(jié)果及證明

[1] Pao C V. Nonlinear parabolic and elliptic equations[M]. New York: Plenum, 1992.

[2] Zhou L, Fu Y. Existence and stability of periodic quasisolutions in nonlinear parabolic systems with discrete delays[J]. J Math Anal Appl, 2000, 250: 139-161.

Uniqueness and attractance of positive periodic solutions in Gilpin-Ayala

ZHANG Jun-jie1MA Man-jun2

(1 School of Mathematics and Physics, University of South China, Hengyang 421001, China;2 College of Sciences, China Jiliang University, Hangzhou 310018, China)

This paper is devoted to the studyGilpin-Ayala model with driven diffusion by applying the method of upper and lower solution and the maximum principle and other analytical techniques. Existence and uniqueness of positive solutions and sufficient conditions for the attractivity of positive periodic of this model are obtained.

the method of upper and lower solution; the maximum principle; uniformly elliptic

O 175

1672-6146(2012)01-0007-04

10.3969/j.issn.1672-6146.2012.01.003

2011-12-08

張俊杰(1986-), 男, 碩士研究生, 研究方向?yàn)槲⒎址匠膛c動(dòng)力系統(tǒng). E-mail: zhangjunjie55@163.com

(責(zé)任編校:劉曉霞)