Open Access Research Article

Exact Multiplicity of Positive Solutions for a Class of Second-Order Two-Point Boundary Problems with Weight Function

Yulian An1* and Hua Luo2

Author Affiliations

1 Department of Mathematics, Shanghai Institute of Technology, Shanghai 200235, China

2 School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China

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Boundary Value Problems 2010, 2010:207649  doi:10.1155/2010/207649

Published: 17 August 2010

Abstract

An exact multiplicity result of positive solutions for the boundary value problems , , , is achieved, where is a positive parameter. Here the function is and satisfies , for for some . Moreover, is asymptotically linear and can change sign only once. The weight function is and satisfies , for . Using bifurcation techniques, we obtain the exact number of positive solutions of the problem under consideration for lying in various intervals in . Moreover, we indicate how to extend the result to the general case.