Electron. J. Diff. Eqns., Vol. 2004(2004), No. 133, pp. 1-8.

Positive solutions for singular semi-positone Neumann boundary-value problems

Yong-Ping Sun, Yan Sun

Abstract:
In this paper, we study the singular semi-positone Neumann bound\-ary-value problem
$$\displaylines{ -u''+m^2u=\lambda f(t,u)+g(t,u),\quad 0 less than t less than 1,\cr u'(0)=u'(1)=0, }$$
where $m$ is a positive constant. Under some suitable assumptions on the functions $f$ and $g$, for sufficiently small $\lambda$, we prove the existence of a positive solution. Our approach is based on the Krasnasel'skii fixed point theorem in cones.

Submitted October 12, 2004. Published November 16, 2004.
Math Subject Classifications: 34B10, 34B15.
Key Words: Positive solution; semi-positone; fixed points; cone; singular Neumann boundary-value problem.

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Yong-Ping Sun
Department of Mathematics, Qufu Normal University
Qufu, Shandong 273165, China.
Department of Fundamental Courses
Hangzhou Radio & TV University
Hangzhou, Zhejiang 310012, China
email: syp@mail.hzrtvu.edu.cn
Yan Sun
Department of Mathematics
Qufu Normal University
Qufu, Shandong 273165, China
email: ysun@163169.net

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