LI Guo-cheng, XUE Xiao-ping, SONG Shi-ji. On the Periodic Solutions of Differential Inclusions and Applications[J]. Applied Mathematics and Mechanics, 2004, 25(2): 150-158.
Citation: LI Guo-cheng, XUE Xiao-ping, SONG Shi-ji. On the Periodic Solutions of Differential Inclusions and Applications[J]. Applied Mathematics and Mechanics, 2004, 25(2): 150-158.

On the Periodic Solutions of Differential Inclusions and Applications

  • Received Date: 2001-07-03
  • Rev Recd Date: 2003-10-08
  • Publish Date: 2004-02-15
  • The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi-linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi-linear differential inclusion.An application to some feedback control systems is discussed.
  • loading
  • [1]
    Aubin J P,Cellina A.Differential Inclusions[M].Berlin:Springer-Verlag,1984.
    Haddad G,Lasry J M.Periodic solution of functional differential inclusions and fixed point of σ-selectionable correspondences[J].J Math Anal Appl,1983,96(2):295—312. doi: 10.1016/0022-247X(83)90042-2
    Macki J,Nistri P,Zecca P.The existence of periodic solutions to nonautonomou differential inclusions[J].Proc Amer Math Soc,1988,104(3):840—844. doi: 10.1090/S0002-9939-1988-0931741-X
    Plaskacz S.Periodic solutions of differential inclusions on compact subsects of RN[J].J Math Anal Appl,1990,148(1):202—212. doi: 10.1016/0022-247X(90)90038-H
    Hu S,Papageorgiou N S.On the existence of periodic solutions for nonconvex valued differential inclusions in RN[J].Proc Amer Math Soc,1995,123(10):3043—3050.
    Hu S,Papageorgiou N S.Periodic solutions for nonconvex differential inclusions[J].Proc Amer Math Soc,1999,127(1):89—94. doi: 10.1090/S0002-9939-99-04338-5
    De Blasi F S,Górniewicz L,Painigiani G.Topological degree and periodic solutions of differential inclusions[J].Nonlinear Anal,1999,37(2):217—245. doi: 10.1016/S0362-546X(98)00044-3
    De Blasi F S,Myjak J.On continuous approximations for multifunctions[J].Pacific J Math,1986,123(1):9—31.
    Klein E,Thompson A.Theory of Correspondences[M].New York:Wiley,1984.
    Papageorgiou N S.A stability result for differential inclusions in Banach spaces[J].J Math Anal Appl,1986,118(1):232—246. doi: 10.1016/0022-247X(86)90305-7
    Dunford N,Schwartz J.Linear Operators[M].New York:Wiley-Interscience,1957.
    Papageorgiou N S.Convergence theorems for Banach space valued integrable multifunctions[J].Internat J Math Sci,1987,10(2):433—442. doi: 10.1155/S0161171287000516
    Hiai F,Umegaki H.Integrals.Conditional expectations and martingales of multivalued functions[J].J Multivariate Anal,1977,7(1):149—182. doi: 10.1016/0047-259X(77)90037-9
    Bressan A,Colombo G.Extensions and selections of maps with decomposable values[J].Studia Math,1988,90(1):69—85.
    LI Guo-cheng,XUE Xiao-ping.On the existence of periodic solutions for differential inclusions[J].J Math Anal Appl,2002,276(1):168—183.[KG*2]. Толстоногов А А.Непрерывные селекторы многозначных отображений с невьшуклыми, незамкнутыми,разложимыми значениями[J].Математическй Сборник,1996,187(5):121—142. doi: 10.1016/S0022-247X(02)00397-9
    Wagner D.Survey on measurable selection theorems[J].SIAM J Control Optim,1977,15(5):859—903. doi: 10.1137/0315056
    Brown L D,Purves R.Measurable selections of extreme[J].Ann Statist,1973,1(2):902—912. doi: 10.1214/aos/1176342510
    Kravvaritis D,Papageorgiou N S.Boundary value problems for nonconvex differential inclusions[J].J Math Anal Appl,1994,185(1):146—160. doi: 10.1006/jmaa.1994.1238
  • 加载中


    通讯作者: 陈斌,
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2619) PDF downloads(590) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint