| Solvability of Multi-Point Boundary Value Problem |
| Received:May 08, 2007 Revised:November 22, 2007 |
| Key Words:
$p$-Laplace multi-point boundary value problem resonance degree theory.
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| Fund Project:the National Natural Science Foundation of China (No.10771212); the Foundation of China University of Mining and Technology (Nos.2005A041; 2006A042; 2008A037). |
| Author Name | Affiliation | | ZHANG Hui Xing | Department of Mathematics, China University of Mining and Technology, Jiangsu 221008, China | | LIU Wen Bin | Department of Mathematics, China University of Mining and Technology, Jiangsu 221008, China | | ZHANG Jian Jun | Department of Mathematics, China University of Mining and Technology, Jiangsu 221008, China | | CHEN Tai Yong | Department of Mathematics, China University of Mining and Technology, Jiangsu 221008, China |
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| Abstract: |
| This paper deals with the existence of solutions for the problem $$\left\{\begin{array}{l}(\phi_p(u'))'=f(t,u,u'),\ \ t \in (0,1),\\ u'(0)=0,\ \ u(1)=\sum_{i=1}^{n-2}a_iu(\eta_i),\end{array}\right.$$ where $\phi_p(s)=|s|^{p-2}s,\ p>1$. $0<\eta_1<\eta_2<\cdots<\eta_{n-2}<1,a_i~(i=1,2,\ldots,n-2)$ are non-negative constants and $\sum_{i=1}^{n-2}a_i=1$. Some known results are improved under some sign and growth conditions. The proof is based on the Brouwer degree theory. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.04.015 |
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