Open Access Research Article

Existence and Uniqueness of Smooth Positive Solutions to a Class of Singular -Point Boundary Value Problems

Xinsheng Du* and Zengqin Zhao

Author Affiliations

School of Mathematics Sciences, Qufu Normal University, Qufu, Shandong 273165, China

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Boundary Value Problems 2009, 2009:191627  doi:10.1155/2009/191627

Published: 1 December 2009

Abstract

This paper investigates the existence and uniqueness of smooth positive solutions to a class of singular m-point boundary value problems of second-order ordinary differential equations. A necessary and sufficient condition for the existence and uniqueness of smooth positive solutions is given by constructing lower and upper solutions and with the maximal theorem. Our nonlinearity may be singular at and/or .