EXISTENCE, MULTIPLICITY AND UNIQUENESS RESULTS FOR A SECOND ORDER M-POINT BOUNDARY VALUE PROBLEM

Let : [0, 1] $\times$ [0, $\infty$) $\longrightarrow$ [0, $\infty$) be continuous and a ${\in}$ C([0, 1], [0, $\infty$)),and let ${\xi}_{i}$ $\in$ (0, 1) with 0 < {\xi}$_1$ < ${\xi}_2$ < … < ${\xi}_{m-2}$ < 1, $a_{i}$, $b_{i}$ ${\in}$ [0, $\infty$) with 0 < $\Sigma_{i=1}$ /$^{m-2}$ $a_{i}$ < 1 and $\Sigma_{i=1}$$^{m-2}$ < l. This paper is concerned with the following m-point boundary value problem: $\chi$″(t)＋a(t) (t.$\chi$(t))＝0,t ${\in}$(0,1), $\chi$'(0)＝$\Sigma_{i=1}$ $^{m-2}$ /$b_{i}$$\chi$'(${\xi}_{i}$),$\chi$(1)＝$\Sigma_{i=1}$$^{m-2}$$a_{i}$$\chi$(${\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.