| 与极大单调算子相关的抽象方程的可解性 |
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| 引用本文： | 魏利. 与极大单调算子相关的抽象方程的可解性[J]. 吉首大学学报(自然科学版), 2004, 25(1): 29-31 |
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| 作者姓名： | 魏利 |
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| 作者单位： | 河北经贸大学数学与统计学学院,河北,石家庄,050091 |
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| 基金项目： | 河北省自然科学基金资助项目(197061)，河北省教育厅科学研究计划项目(2000405) |
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| 摘 要： | 设X是实自反、严格凸Banach空间,其对偶空间X 是一致凸空间,T:D(T) XX 是极大单调算子,C:D(T) XX 是连续、有界映射.利用非线性泛函分析中的Leray-Schauder度理论,给出了带扰动的极大单调算子方程(T+C)x=f在抽象空间X中解的存在性的一些新的判别条件.
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| 关 键 词： | 单调算子 紧映射 对偶映射 |
| 文章编号： | 1007-2985(2004)01-0029-03 |
| 修稿时间： | 2003-04-28 |
The Solvability of Abstract Equation Involving the Maximal Monotone Operator |
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| WEI Li. The Solvability of Abstract Equation Involving the Maximal Monotone Operator[J]. Journal of Jishou University(Natural Science Edition), 2004, 25(1): 29-31 |
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| Authors: | WEI Li |
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| Affiliation: | ( College of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050091,Hebei China) |
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| Abstract: | Let X be a real reflexive,strictly convex Banach space with its dual space X~* being uniformly convex,T be a maximal monotone operator from D(T)X to X~*,and C a continuous and bounded mapping from D(T)X to X~*.Used by Leray-Schauder's topology degree theory in nonlinear analysis,some new results are given to study the existence of solution of the operator equation (T+C)x=f involving the maximal monotone operator T with the perturbation C in an abstract space X. |
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| Keywords: | monotone operator compact mapping duality mapping |
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