ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (2): 168-177.

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

李国成¹, 薛小平¹, 宋士吉²

1. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China;
2. Department of Automation, Tsinghua University, Beijing 100084, P. R. China

收稿日期:2001-07-03 修回日期:2003-10-08 出版日期:2004-02-18 发布日期:2004-02-18
通讯作者: XUE Xiao-ping(Corresponding author)(Tel:86-0451-86471744(O), 86-0451-86416030(H), E-mail:xiaopingxue@263.net) E-mail:xiaopingxue@263.net

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

LI Guo-cheng¹, XUE Xiao-ping¹, SONG Shi-ji ²

1. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China;
2. Department of Automation, Tsinghua University, Beijing 100084, P. R. China

Received:2001-07-03 Revised:2003-10-08 Online:2004-02-18 Published:2004-02-18

摘要/Abstract

摘要： 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.

中图分类号:

李国成;薛小平;宋士吉. ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(2): 168-177.

LI Guo-cheng;XUE Xiao-ping;SONG Shi-ji . ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(2): 168-177.

参考文献

[1] Aubin J P, Cellina A. Differential Inclusions [M]. Berlin:Springer-Verlag, 1984.
[2] Haddad G, Lasry J M. Periodic solution of functional differential inclusions and fixed point of ó-selectionable correspondences[J]. J Math Anal Appl, 1983, 96(2):295-312.
[3] 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.
[4] Plaskacz S. Periodic solutions of differential inclusions on compact subsects of RN[J]. J Math Anal Appl, 1990, 148(1):202-212.
[5] Hu S, Papageorgiou N S. On the existence of periodic solutions for nonconvex valued differential inclusions in RN[J]. Proc Amer Math Soc, 1995, 123 (10):3043-3050.
[6] Hu S, Papageorgiou N S. Periodic solutions for nonconvex differential inclusions[J]. Proc Amer Math Soc, 1999, 127(1):89-94.
[7] De Blasi F S, Gorniewicz L, Painigiani G. Topological degree and periodic solutions of differential inclusions[J]. Nonlinear Anal, 1999, 37(2):217-245.
[8] De Blasi F S, Myjak J. On continuous approximations for multifunctions[J]. Pacific J Math, 1986, 123(1):9-31.
[9] Klein E, Thompson A. Theory of Correspondences [M]. New York:Wiley, 1984.
[10] PapageorgiouN S. Astability result for differential inclusions in Banach spaces[J]. J Math Anal Appl, 1986, 118(1):232-246.
[11] Dunford N, Schwartz J. Linear Operators[M]. New York:Wiley-Interscience, 1957.
[12] Papageorgiou N S. Convergence theorems for Banach space valued integrable multifunctinns[J]. Internat J Math Sci, 1987, 10(2):433-442.
[13] Hiai F, Umegaki H. Integrals. Conditional expectations and martingales of multivalued functions[J]. J Multivariate Anal, 1977, 7(1):149-182.
[14] Bressan A, Colombo G. Extensions and selections of maps with decomposable values[J]. Studia Math, 1988, 90(1):69-85.
[15] LI Guo-cheng, XUE Xiao-ping. On the existence of periodic solutions for differential inclusions[J]. J Math AnalAppl, 2002, 276(1):168-183.
[16] Толстоногов А А. Heпpepывные селекторы многозначных отображений с невьШуклыми, незамкнутымн, разложимымн значениями[J]. Мамемамццескй Сборнцк, 1996, 187(5):121-142.
[17] Wagner D. Survey on meseurable selection theorems[J]. SIAM J Control Optim, 1977, 15(5):859-903.
[18] Brown L D, Purves R. Measurable selections of extreme[J]. Ann Statist, 1973, 1(2):902-912.
[19] Kravvaritis D, Papageorgiou N S. Boundary value problems for nonconvex differential inclusions[J]. J Math AnalAppl, 1994, 185(1):146-160.

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	陈丽华;莫嘉琪. Singularly perturbed solution for weakly nonlinear equations with two parameters[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(10): 1343-1348 .
[2]	张韧;洪梅;孙照渤;牛生杰;朱伟军;闵锦忠;万齐林. NON-LINEAR DYNAMIC MODEL RETRIEVAL OF SUBTROPICAL HIGH BASED ON EMPIRICAL ORTHOGONAL FUNCTION AND GENETIC ALGORITHM[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(12): 1645-1653 .
[3]	袁玉波;溥冬梅;李庶民. BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS IN VARIANT BOUSSINESQ EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(6): 811-822 .
[4]	马军海;王志强;陈予恕. PREDICTION TECHNIQUES OF CHAOTIC TIME SERIES AND ITS APPLICATIONS AT LOW NOISE LEVEL[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(1): 7-14 .
[5]	骆海英;李继彬. WHAT ARE THE SEPARATRIX VALUES NAMED BY LEONTOVICH ON HOMOCLINIC BIFURCATION[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(4): 457-464 .
[6]	马军海;任彪;陈予恕. ANALYSIS AND APPLIED STUDY OF DYNAMIC CHARACTERISTICS OF CHAOTIC REPELLER IN COMPLICATED SYSTEM[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(4): 449-456 .
[7]	莫嘉琪;王辉. SHIFT OF SHOCK POSITION FOR A CLASS OF NONLINEAR SINGULARLY PERTURBED PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(1): 58-62 .
[8]	马军海;任彪;陈予恕. IMPULSIVE CONTROL OF CHAOTIC ATTRACTORS IN NONLINEAR CHAOTIC SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(9): 971-976.
[9]	马军海;陈予恕;辛宝贵. STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(6): 605-611.
[10]	廖世俊. ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(1): 53-60.
[11]	刘俊. RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(10): 1229-1236.
[12]	何吉欢. LINEARIZATION AND CORRECTION METHOD FOR NONLINEAR PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(3): 241-248.
[13]	马军海;陈予恕. STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅱ)[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(12): 1375-1382.
[14]	西密尔&#;通兹. BOUNDEDNESS AND UNIFORM BOUNDEDNESS RESULTS FOR CERTAIN NON-AUTONOMOUS DIFFERENTIAL EQUATIONS OF FOURTH ORDER[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(11): 1273-1278.
[15]	马军海;陈予恕. STUDY ON THE PREDICTION METHOD OF LOW-DIMENSION TIME SERIES THAT ARISE FROM THE INTRINSIC NONLINEAR DYNAMIC[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(5): 501-509.