| 渐近线性算子方程的四种类型的解 |
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| 引用本文： | 张克梅,孙经先.渐近线性算子方程的四种类型的解[J].数学学报,2007,50(6):1403-141. |
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| 作者姓名： | 张克梅 孙经先 |
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| 作者单位： | 曲阜师范大学数学科学学院，徐州师范大学数学系 曲阜 273165，徐州 221116 |
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| 基金项目： | 国家自然科学基金(10671167，10471075) |
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| 摘 要： | 利用拓扑度理论及不动点指数理论,讨论了渐近线性算子方程的四种类型的解(即零解、正解、负解和变号解)的存在性,并将这一抽象结果应用于微分方程两点边值问题.
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| 关 键 词： | 不动点指数 变号解 正解 负解 |
| 文章编号： | 0583-1431（2007）06-1403-08 |
| 收稿时间： | 2006-9-11 |
| 修稿时间： | 2006-09-11 |
Four Kinds of Solutions for Asymptotically Linear Operator Equations and Its Applications |
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| Ke Mei ZHANG, Jing Xian SUN.Four Kinds of Solutions for Asymptotically Linear Operator Equations and Its Applications[J].Acta Mathematica Sinica,2007,50(6):1403-141. |
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| Authors: | Ke Mei ZHANG Jing Xian SUN |
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| Institution: | 1.Department of Mathematics, Qufu Normal University, Qufu 273165, P. R. China;2. Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, P. R. China |
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| Abstract: | In this paper,by using the topological degree theory and the fixed point index theory,the existence of four kinds of solutions(i.e.,zero solution,positive solu- tion,negative solution and sign-changing solution)for asymptotically linear operator equations is discussed,and the abstract results are applied to two-point boundary value problems for differential equations. |
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| Keywords: | fixed point index positive solution negative solution sign-changing solution |
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