# EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR SINGULAR THREE-POINT BOUNDARY VALUE PROBLEMS

• Miao, Chunmei (Department of Applied Mathematics, Beijing Institute of Technology, College of Science, Changchun University) ;
• Ge, Weigao (Department of Applied Mathematics, Beijing Institute of Technology)
• Published : 2009.05.31

#### Abstract

In this paper, the singular three-point boundary value problem $$\{{{u"(t)\;+\;f(t,\;u)\;=\;0,\;t\;{\in}\;(0,\;1),}\atop{u(0)\;=\;0,\;u(1)\;=\;{\alpha}u(\eta),}}\$$ is studied, where 0 < $\eta$ < 1, $\alpha$ > 0, f(t,u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results.

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