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<p/> <p>By using the fixed-point index theory and Leggett-Williams fixed-point theorem, we study the existence of multiple solutions to the three-point boundary value problem <inline-formula><graphic file="1687-1847-2011-894135-i1.gif"/></inline-formula>,&#8201;&#8201;<inline-formula><graphic file="1687-1847-2011-894135-i2.gif"/></inline-formula>; <inline-formula><graphic file="1687-1847-2011-894135-i3.gif"/></inline-formula>; <inline-formula><graphic file="1687-1847-2011-894135-i4.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2011-894135-i5.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2011-894135-i6.gif"/></inline-formula> are constants, <inline-formula><graphic file="1687-1847-2011-894135-i7.gif"/></inline-formula> is a parameter, and <inline-formula><graphic file="1687-1847-2011-894135-i8.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2011-894135-i9.gif"/></inline-formula> are given functions. New existence theorems are obtained, which extend and complement some existing results. Examples are also given to illustrate our results.</p>