| 2p和2q阶联立微分方程组的正解性 |
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| 引用本文： | 杨瑞兰,张炎彪. 2p和2q阶联立微分方程组的正解性[J]. 系统科学与数学, 2009, 29(12): 1571-1578 |
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| 作者姓名： | 杨瑞兰 张炎彪 |
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| 作者单位： | 忻州师范学院数学系,忻州,034000 |
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| 摘 要： | 利用锥上不动点指数理论研究2p,2q阶非线性高阶常微分方程组边值问题,通过相应的线性问题的第一特征值,建立了其正解的存在性与多解性定理.讨论了其参数$lambda,mu$对其正解存在性与多解性的影响,给出了利用特征值刻划的较为本质的结果.突破了以往文献要求方程组同阶和非线性项单调,在零点或无穷远点超线性或次线性增长的限制.
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| 关 键 词： | 常微分方程组 边值问题 锥 不动点指数理论 正解. |
| 收稿时间： | 2008-09-13 |
POSITIVE SOLUTIONS FOR 2p AND 2q ORDER SIMULTANEOUS NONLINEAR ORDINARY DIFFERENTIAL SYSTEM |
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| YANG Ruilan,ZHANG Yanbiao. POSITIVE SOLUTIONS FOR 2p AND 2q ORDER SIMULTANEOUS NONLINEAR ORDINARY DIFFERENTIAL SYSTEM[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(12): 1571-1578 |
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| Authors: | YANG Ruilan ZHANG Yanbiao |
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| Affiliation: | Department of Mathematics, Xin Zhou Teachers University, Xinzhou 034000 |
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| Abstract: | In this paper, the authors study the existence and multiplicity of two point BVP for 2p and 2q order simultaneous nonlinear ordinary differential systems by using the fixed-point index theory. The existence and mulitiplicity theorems on positive solutions are established by using the first eigenvalue of the corresponding linear problems. |
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| Keywords: | Nonlinear ordinary differential systems boundary value problems cone fixed point index theory positive solution. |
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