Electron. J. Diff. Eqns., Vol. 2008(2008), No. 116, pp. 1-20.

Positive solutions for singular three-point boundary-value problems

Ravi P. Agarwal, Donal O'Regan, Baoqiang Yan

Using the theory of fixed point index, this paper discusses the existence of at least one positive solution and the existence of multiple positive solutions for the singular three-point boundary value problem:
 y''(t)+a(t)f(t,y(t),y'(t))=0,\quad 0<t<1,\cr
 y'(0)=0,\quad y(1)=\alpha y(\eta),
where $0<\alpha<1$, $0<\eta<1$, and $f$ may be singular at $y=0$ and $y'=0$.

Submitted January 17, 2008. Published August 25, 2008.
Math Subject Classifications: 34B15.
Key Words: Three-point boundary value problems; singularity; positive solutions; fixed point index.

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Ravi P. Agarwal
Department of Mathematical Science
Florida Institute of Technology
Melbourne, Florida 32901, USA
email: agarwal@fit.edu
Donal O'Regan
Department of Mathematics, National University of Ireland
Galway, Ireland
email: donal.oregan@nuigalway.ie
  Baoqiang Yan
Department of Mathematics, Shandong Normal University
Ji-nan, 250014, China
email: yanbqcn@yahoo.com.cn

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