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
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