Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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TRIPLE POSITIVE SOLUTIONS OF SECOND ORDER SINGULAR NONLINEAR THREE-POINT BOUNDARY VALUE PROBLEMS

  • Sun, Yan (Department of Mathematics, Shanghai Normal University)
  • Received : 2009.09.10
  • Accepted : 2009.10.18
  • Published : 2010.05.30
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Abstract

This paper deals with the existence of triple positive solutions for the nonlinear second-order three-point boundary value problem z"(t)+a(t)f(t, z(t), z'(t))=0, t $\in$ (0, 1), $z(0)={\nu}z(1)\;{\geq}\;0$, $z'(\eta)=0$, where 0 < $\nu$ < 1, 0 < $\eta$ < 1 are constants. f : [0, 1] $\times$ [0, $+{\infty}$) $\times$ R $\rightarrow$ [0, $+{\infty}$) and a : (0, 1) $\rightarrow$ [0, $+{\infty}$) are continuous. First, Green's function for the associated linear boundary value problem is constructed, and then, by means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of triple positive solutions to the boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order derivative explicitly.

Keywords

Acknowledgement

Supported by : Shanghai Normal University, Shanghai Municipal Education Commission

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