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 Existence, multiplicity and uniqueness results for a second order m-point boundary value problem Bull. Korean Math. Soc. 2004 Vol. 41, No. 3, 483-492 Published online September 1, 2004 Yuqiang Feng and Sanyang Liu Xidian University, Xidian University Abstract : Let $f:[0,1]\times [0,\infty)\rightarrow [0,\infty)$ be continuous and $a\in C([0,1],[0,\infty))$,and let $\xi_{i}\in (0,1)$ with $0<\xi_{1} <\xi_{2}<\cdots<\xi_{m-2}<1,a_{i}, b_{i}\in [0,\infty)$ with $0<\sum_{i=1}^{m-2}a_{i}<1$ and $\sum_{i=1}^{m-2}b_{i}<1$.This paper is concerned with the following m-point boundary value problem: $$x^{''}(t)+a(t)f(t,x(t))=0, t\in (0,1),$$ $$x^{'}(0)=\sum_{i=1}^{m-2}b_{i}x^{'}(\xi_{i}), x(1)=\sum_{i=1}^{m-2}a_{i}x(\xi_{i}) .$$ The existence, multiplicity and uniqueness of positive solutions of this problem are discussed with the help of two fixed point theorems in cones, respectively. Keywords : m-point boundary value problem, existence of positive solutions, multiplicity, uniqueness MSC numbers : 34B15 Downloads: Full-text PDF