| 奇异非线性Sturm-Liouville问题的正解 |
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| 引用本文： | 孙经先,张国伟.奇异非线性Sturm-Liouville问题的正解[J].数学学报,2005,48(6):1095-1104. |
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| 作者姓名： | 孙经先 张国伟 |
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| 作者单位： | [1]徐州师范大学数学系,徐州221116 [2]东北大学数学系,沈阳110004 |
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| 基金项目： | 国家自然科学基金资助项目（10371066;10371013） |
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| 摘 要： | 本文研究奇异非线性Sturm-Liouville问题其中(Lφ)(x)=(p(x)φ′(x))′+g(x)φ(x),并且允许h(x)在x=0和x=1奇异。应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下获得了正解的存在性结果,本质地推广和改进了文献1-9]中的主要结论。
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| 关 键 词： | 奇异 非线性Sturm-Liouville问题 正解 |
| 文章编号： | 0583-1431（2005）06-1095-10 |
| 收稿时间： | 2003-06-04 |
| 修稿时间： | 2003-06-042004-11-11 |
Positive Solutions of Singular Nonlinear Sturm-Liouville Problems |
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| Jing Xian SUN, Guo Wei ZHANG.Positive Solutions of Singular Nonlinear Sturm-Liouville Problems[J].Acta Mathematica Sinica,2005,48(6):1095-1104. |
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| Authors: | Jing Xian SUN Guo Wei ZHANG |
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| Institution: | 1 Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, P. R. China;2 Department of Mathematics, Northeastern University, Shenyang 110004, P. R. China |
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| Abstract: | The singular nonlinear Sturm-Liouville problem is considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where (L_φ)(x)=(p(x)φ'(x))'+q(x)φ(x) and h(x) is allowed to be singular at both x=0 and x=1. The existence results of positive solutions are given by means of the cone theory and the fixed point index. The conclusions in this paper essentially extend and improve the main results in 1-9]. |
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| Keywords: | Singular Nonlinear Sturm-Liouville problems Positive solutions |
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