**Existence of positive solutions for nth-order boundary value problem with sign changing nonlinearity**

**Dapeng Xie**, Yanbian University, Yanji, Jilin, P. R. China**Chuanzhi Bai**, Huaiyin Teachers College, Huaian, Jiangsu, P. R. China**Yang Liu**, Yanbian University, Yanji, Jilin, P. R. China**Chunli Wang**, Yanbian University, Yanji, Jilin, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 8. (2008), pp. 1-10.

Communicated by P. Eloe.
| Received on 2007-08-17 Appeared on 2008-02-11 |

**Abstract: **In this paper, we investigate the existence of positive solutions for singular $n$th-order boundary value problem $u^{(n)}(t)+a(t)f(t,u(t))=0,\quad 0\le t\le1,$ $u^{(i)}(0)=u^{(n-2)}(1)=0,\quad 0\le i\le n-2,$ where $n\ge2$, $a\in C((0,1),[0,+\infty))$ may be singular at $t=0$ and (or) $t=1$ and the nonlinear term $f$ is continuous and is allowed to change sign. Our proofs are based on the method of lower solution and topology degree theorem.

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