Electron. J. Diff. Eqns., Vol. 2007(2007), No. 03, pp. 1-9.

Positive solutions for singular nonlinear beam equation

Ruhao Song, Haishen Lu

Abstract:
In this paper, we study the existence of solutions for the singular p-Laplacian equation
$$\displaylines{ \big(|u''|^{p-2}u''\big)''-f(t,u)=0,\quad t\in (0,1) \cr u(0)=u(1)=0, \cr u''(0)=u''(1)=0, }$$
where $f(t,u)$ is singular at $t=0,1$ and at $u=0$. We prove the existence of at least one solution.

Submitted November 13, 2006. Published January 2, 2007.
Math Subject Classifications: 34B15, 34B16.
Key Words: p-laplacian; singular; fixed point theorem.

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Ruhao Song
Department of Applied Mathematics
Hohai University
Nanjing 210098, China
email: songruhao@163.com
Haishen Lu
Department of Applied Mathematics
Hohai University
Nanjing 210098, China
email: haishen2001@yahoo.com.cn

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