Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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EXISTENCE, MULTIPLICITY AND UNIQUENESS RESULTS FOR A SECOND ORDER M-POINT BOUNDARY VALUE PROBLEM

  • Feng, Yuqiang (Department of Applied Mathematics, Xidian University) ;
  • Liu, Sang-Yang (Department of Applied Mathematics, Xidian University)
  • Published : 2004.08.01
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Abstract

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.

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Cited by

  1. Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation vol.2012, 2012, https://doi.org/10.1155/2012/489353
  2. Monotone positive solutions of second-order multi-point boundary value problems vol.207, pp.2, 2009, https://doi.org/10.1016/j.amc.2008.11.004