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一类互惠模型正解的存在性 被引量：4

Existence of positive solutions for a cooperative model
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摘要 利用正的紧线性微分算子的谱性质和锥映象不动点指标,结合极值原理和上下解方法,研究了具有饱和项的Volterra-Lotka互惠模型的平衡态方程,得到了具有饱和项的互惠模型正解存在的充分条件. By using the spectral properties of positive compact linear differential opetators and fixed points index of compact maps in cones, combining with maximum principles and lower-upper solutions method, the steady-state equation of a kind of the Volterra-Lotka cooperative model with saturation is studied, sufficient conditions for the existence of positive solutions of the system are obtained.
作者 解玉龙 李艳玲
机构地区 陕西师范大学数学与信息科学学院
出处 《西北师范大学学报（自然科学版）》 CAS 2007年第6期6-10,共5页 Journal of Northwest Normal University(Natural Science)
基金 国家自然科学基金资助项目(10571115)
关键词 平衡解 谱 不动点指标 上下解 steady-state solution spectrum fixed points index lower-upper solutions
分类号 O175.26 [理学—基础数学]
  • 相关文献

参考文献9

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共引文献22

同被引文献44

  • 1袁正光.数字革命：一场新的经济战─—世界数字技术发展的趋势及我们的对策[J].自然辩证法研究,1994,10(4):1-7. 被引量：17
  • 2黑力军.一类具有扩散的互惠共食系统的存在性和全局吸引性[J].应用数学,2005,18(4):594-602. 被引量：1
  • 3Li Z Y,De Mottoni P.Bifurcation for some systems of cooperative and predator-prey type[J].J Partial Differential Equations,1992,5:25-36.
  • 4Lou Y.Necessary and sufficient condition for the existence of positive solutions of certain cooperative system[J].Nolinear Anal,1996,26:1079-1095.
  • 5Korman P,Leung A.On the existence and uniqueness of positive steady states in the Volterra-Lotka ecological models with diffusion[J].Appl Anal,1987,26(02):145-160.
  • 6Kim K I,Lin Z G.Blowup in a three-species cooperating model[J].Applied Mathematics with Application,2002,43:1277-1290.
  • 7Wu J H.Coexistence state for cooperative model with diffusion[J].Computers and Mathematics with Applications,2002,43:1279-1290.
  • 8Smoller Joel.Shock Waves and Reaction-Diffusion Equations[M].New York:Springer-Verlag,1983.
  • 9Du Y H,Lou Y.Qualitative behaviour of positive solutions ofa predator-prey model:Effects of saturation[J].Journal of Proceedings of the Royal Society of Edinburgh,2001,131:321-349.
  • 10Korman P, Leung A. On the existence and uniqueness of positive steady state in the Voherra-Lotka ecological models with diffusion .Application Analysis, 1987 ;26 : 145--160.

引证文献4

二级引证文献15

西北师范大学学报（自然科学版）
2007年 第6期

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