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

• Mathematics •     Next Articles

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)

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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