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

Abstract:
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:
$$\displaylines{ y''(t)+a(t)f(t,y(t),y'(t))=0,\quad 0<t<1,\cr y'(0)=0,\quad y(1)=\alpha y(\eta), }$$
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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