journal6 ›› 2012, Vol. 33 ›› Issue (6): 1-9.DOI: 10.3969/j.issn.1007-2985.2012.06.001

• 数学 •    下一篇



  1. (南京财经大学应用数学系,江苏 南京 210003)
  • 出版日期:2012-11-25 发布日期:2013-01-14

Positive Solutions of Second-Order Singular Differential Equations with Dirichlet Boundary Condition

  1. (Department of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210003,China)
  • Online:2012-11-25 Published:2013-01-14
  • About author:YAO Qing-liu(1946-),male,was born in Shanghai City,professor;research area is applied differential equations.
  • Supported by:

    National Natural Science Foundation of China (11071109)

摘要:研究了非线性2阶Dirichlet 边值问题u″(t)-λu(t)+h(t)f(t,u(t))+g(t,u(t))=00<t<1,u(0)=u(1)=0的正解存在性与多解性,其中λ>-π2是常数,而g(t,u)可以在u=0处奇异.通过精确估计解的先验界并且利用锥拉伸-压缩的Guo-Krasnoselskii不动点定理,建立了几个存在定理.

关键词: 非线性常微分方程, 奇异边值问题, 正解, 存在性与多解性

Abstract: The existence and multiplicity of positive solutions are studied for the nonlinear second-order Dirichlet boundary value problem u″(t)-λu(t)+h(t)f(t,u(t))+g(t,u(t))=00<t<1,u(0)=u(1)=0,where λ>-π2 is a constant and g(t,u) may be singular at u=0.By exactly estimating the priori bound of solution and applying the Guo-Krasnoselskii fixed point theorem of cone expansion-compression type,several existence theorems are established.

Key words: nonlinear ordinary differential equation, singular boundary value problem, positive solution, existence and multiplicity

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