中山大学学报自然科学版 ›› 2012, Vol. 51 ›› Issue (1): 14-18.

• 研究论文 • 上一篇    下一篇

带交叉扩散项的捕食模型非常数正解的存在性

王利娟1,2,姜洪领2   

  1. (1. 陕西师范大学数学与信息科学学院,陕西 西安 710062; 2. 宝鸡文理学院数学系,陕西 宝鸡 721013 )
  • 收稿日期:2011-05-19 修回日期:1900-01-01 出版日期:2012-01-25 发布日期:2012-01-25

The Existence of Nonconstant Positive Solution for a Prey-Predator Model with Cross-Diffusion

WANG Lijuan1,2, JIANG Hongling2   

  1. (1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China;〖JP〗2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China)
  • Received:2011-05-19 Revised:1900-01-01 Online:2012-01-25 Published:2012-01-25

摘要: 讨论了一类具有交叉扩散项的捕食食饵模型正解的存在性。利用最大值原理和Harnack不等式给出了模型正解的先验估计,运用积分性质证明了非常数正解的不存在性,再利用度理论得到了非常数正解存在的充分条件。

关键词: 交叉扩散, 非常数正解, 度理论

Abstract: The existence of positive solutions is discussed for a prey-predator model with cross-diffusion. The prior estimate to the positive solutions of the model is given by means of maximum principle and Harnack inequality. By using the integral property, the nonexistence of the nonconstant positive solutions is proved. The sufficient conditions for the existence of nonconstant positive solutions are obtained.

Key words: cross-diffusion, nonconstant positive solution, degree theory

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