微分包含的周期生存轨道

Periodic Viable Trajectories of Differential Inclusions

Institute of Economics, Shangdong Electric Power Research Institute, Jinan 250002, P R China

摘要: 对微分包含的周期生存轨道进行了研究讨论。首先给出微分包含生存问题的一约化性质;然后,利用投影微分包含的方法给出有限维空间中微分包含的周期生存轨道的一个存在性结果;在此基础上,利用Galerkin逼近方法得到Hilbert空间中偏微分包含周期生存轨道的存在性定理。
- 微分包含 /
- 相依锥 /
- 生存轨道 /
- Galerkin方法
Abstract: In this paper,the periodic viable trajectories of differential inclusions are discussed.Firstly,a simplified property of differential inclusions is given. Then,an existence theorem of periodic viable trajectories of differential inclu sions in a finite dimensional space is proved.With the above results and Galerkin's approximation,an existence theorem of periodic viable trajectories of partial differential inclusions in a Hilbert space is proved.
- differential inclusion /
- contingent cone /
- viable trajectory /
- Galerkin approximation

[1]	Aubin J P,Cellina A.Differential Inclusions[M].New York:Springer-Verlag,1984.
[2]	Aubin J P.Viability Theory[M].Boston:Birkauser,1991.
[3]	Aubin J P,Frankowska H.Set-Valued Analysis[M].Boston:Birkauser,1992.
[4]	Frankowska H.Plaskacz S.A measurable upper semicontinuous viability for tubes[J].Nonlinear Analysis,TMA,1996,26(3):565~582.
[5]	Li Xunjing.Dif erential Equation Theory of Optimal Control[M],Beijing:Hinger Education Press,1989.(in Chinese)
[6]	Guo Dajun,Sun Jingx ian.Dif erential Equations in Abstract Spaces[M].Jinan:Shandong Science and Technology Press,1989.(in Chinese)
[7]	Aubin J P.Applied Functional Analysis[M].New York:Wiley-Interscience,1977.
[8]	Shi Shuzhong.Nagumo type conditions for partial differential inclusions[J].Nonlinear Analysis TMA,1988,12(9):951~957.
[9]	Zeidler E.Nonlinear Functional Analysis and Its Applications[M].Vol.2,New York:Springer-Verlag,1990.