| Banach空间中一类周期非线性受控系统最优控制的存在性 |
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| 引用本文： | 韦维,P.Sattayathm. Banach空间中一类周期非线性受控系统最优控制的存在性[J]. 应用泛函分析学报, 2002, 4(2): 124-136 |
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| 作者姓名： | 韦维 P.Sattayathm |
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| 作者单位： | 1. 贵州大学数学系,贵州,贵阳,550025
2. 苏南拉里理工大学,泰国,呵叻,30000 |
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| 基金项目： | Supported by Guizhou Provincial President Grant(2001055) |
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| 摘 要： | 研究一类强非线性发展方程的周期解及相应的最优控制问题的存在性，首先，证明了Banach空间中一类包含非线性单调算子和非线性非单调扰动的强非线性发展方程周期解的存在性；其次，给出了保证相应的Lagrange最优控制的充分条件；最后，举例说明理论结果在拟线笥抛物方程周期问题及相应的最优控制问题中的应用。
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| 关 键 词： | Banach空间 周期非线性受控系统 最优控制 存在性 非线性发展方程 周期解 单调算子 |
On Existence of Optimal Control Governed by a Class of Periodic Nonlinear Evolution Systems on Banach Spaces |
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| WEI Wei,P.Sattayathm. On Existence of Optimal Control Governed by a Class of Periodic Nonlinear Evolution Systems on Banach Spaces[J]. Acta Analysis Functionalis Applicata, 2002, 4(2): 124-136 |
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| Authors: | WEI Wei P.Sattayathm |
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| Abstract: | In this paper, we prove an existence of periodic solutions of strongly nonlinear evolution equation containing a nonlinear monotone operator and a nonlinear nonmonotone perturbation in Banach spaces. Existence of Lagrange optimal control problem governed by periodic systems on Banach spaces is also presented. For illustration, an example of a quasi-linear parabolic differential equation and corresponding to optimal control problem is also discussed. |
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| Keywords: | nonlinear evolution equation periodic solution monotone operator optimal control quasi-linear parabolic differential equation |
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