Existence of Positive Solutions of Nonlinear Second-Order M-Point Boundary Value Problem

Existence of Positive Solutions of Nonlinear Second-Order M-Point Boundary Value Problem

F. H. Wong (National Taipei University of Education, Taiwan), C. J. Chyan (Tamkang University, Taiwan) and S. W. Lin (Tamkang University, Taiwan)
Copyright: © 2011 |Pages: 6
DOI: 10.4018/jalr.2011010103
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Abstract

Under suitable conditions on, the nonlinear second-order m-point boundary value problem has at least one positive solution. In this paper, the authors examine the positive solutions of nonlinear second-order m-point boundary value problem.
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Introduction

The study of multi-point boundary value problems for linear second-order ordinary value problems was initialed by Llyin and Moisser (1987). Then Gupta studied three-point boundary value problems for nonlinear ordinary differential equations. We refer the reader to the reference (Gupta et al., 1994; Feng et al., 1997; Ma, 2001; Sun, 2005) for some recent results of nonlinear multi-point boundary value problems.

In this paper, we investigate the existence of positive solutions to nonlinear second-order multi-point boundary value problems:, (1.1), (1.2) where for and , satisfy and . We also make the following assumptions.

()

() There are real numbers , satisfying on and on , where and or

() there are real numbers , satisfying on and on .

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