Electron. J. Diff. Equ., Vol. 2009(2009), No. 115, pp. 1-11.

Upper and lower solutions for a second-order three-point singular boundary-value problem

Qiumei Zhang, Daqing Jiang, Shiyou Weng, Haiyin Gao

Abstract:
We study the singular boundary-value problem
$$\displaylines{ u''+ q(t)g(t,u)=0,\quad t \in (0,1),\; \eta \in (0,1),\;\gamma >0\cr u(0)=0, \quad u(1)=\gamma u(\eta)\,. }$$
The singularity may appear at $ t=0$ and the function $g$ may be superlinear at infinity and may change sign. The existence of solutions is obtained via an upper and lower solutions method.

Submitted January 27, 2009. Published September 12, 2009.
Math Subject Classifications: 34B15, 34B16.
Key Words: Singular boundary-value problem; upper and lower solutions; existence of solutions; superlinear.

Editors note (December 22, 2009):
The result here seems to be particular case of results previously published by the first two authors (using exactly the same methods).
Qiumei Zhang, Daqing Jiang, Upper and lower solutions method and a second order three-point singular boundary value problem, Computers and Mathematics with Applications 56 (2008) 1059-1070. (Received 26 July 2007; accepted 7 January 2008).
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Qiumei Zhang
School of Science, Changchun University,
Changchun 130022, China.
Department of Mathematics, Northeast Normal University
Changchun 130024, China
email: zhangqm1110@yahoo.com.cn
Daqing Jiang
Department of Mathematics, Northeast Normal University
Changchun 130024, China
email: jiangdq067@nenu.edu.cn
Haiyin Gao
School of Science, Changchun University
Changchun 130022, China
email: gaohaiyinhealthy@yahoo.com.cn
Shiyou Weng
School of Science, Changchun University
Changchun 130022, China
email: wengshiyou2001@yahoo.com.cn

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