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.

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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