Copyright © 2010 Chuanzhi Bai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

With the help of the fixed point index theorem in cones, we get an existence theorem concerning the existence of positive solution for a second-order three-point eigenvalue problem x′′(t)+λf(t,x(t))=0,  0≤t≤1,  x(0)=0,  x(1)=x(η), where λ is a parameter. An illustrative example is given to demonstrate the effectiveness of the obtained result.