Cemil Tun. Boundedness and Uniform Boundedness Results for Certain Non-Autonomous Differential Equations of Fourth Order[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1147-1152.
Citation: Cemil Tun. Boundedness and Uniform Boundedness Results for Certain Non-Autonomous Differential Equations of Fourth Order[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1147-1152.

Boundedness and Uniform Boundedness Results for Certain Non-Autonomous Differential Equations of Fourth Order

  • Received Date: 2000-11-13
  • Rev Recd Date: 2001-04-08
  • Publish Date: 2001-11-15
  • Sufficient conditions have been obtained so that all solutions of a different fourth order differential equation are bounded and uniformly bounded.
  • loading
  • [1]
    Liapunov A M. Stability of Motion[M]. London: Academic Press,1966.
    [2]
    Reissig R, Sansone G, Conti R. Nonlinear Differential Equations of Higher Order[M]. Noordhoff International Publishing,1974.
    [3]
    Abou-EI-EIa A M A, Sadek A I. On the asymptotic behaviour of solutions of some differential equations of the fourth order[J]. Ann Differential Equations,1992,8(1):1-12.
    [4]
    Hara T. On the asymptotic behavior of the solutions of some third and fourth order non-autonomous differential equations[J]. Publ RIMS Kyoto Univ,1974,9:649-673.
    [5]
    JIN Jun. On the uniform boundedness of the solution of the non-linear differential equation of the fourth order[J]. Ann Differential Equations,1988,4(2):159-171.
    [6]
    Saded A I. On the asymptotic behaviour of solutions of certain fourth order ordinary differential equations[J]. Math Japon,1997,45(3):527-540.
    [7]
    Tunc,, C. On the asymptotic behaviour of solutions of some differential equations of the fourth order[J]. Studia Univ Babes-Bolyai Math,1994,39(2):87-96.
    [8]
    Tunc,, C. On the asymptotic behaviour of solutions of certain fourth order non-autonomous differential equations[J]. Studia Univ Babes-Bolyai Math,1996,41(3):95-105.
    [9]
    Tunc,, C. On the uniform boundedness of solutions of some non-autonomous differential equations of the fourth order[J]. Appl Math Mech(English Ed),1999,20(6):622-628.
    [10]
    Lasalle J, Lefschetz S. Stability by Liapunov's Direct Method With Applications[M]. New York: Academic Press,1961.
    [11]
    Yoshizawa T. Stability theory by Liapunov's second method[Z]. The Mathematical Society of Japan,1966.
    [12]
    Ezeilo J O C. On the boundedness and the stability of solutions of some differential equations of the fourth order[J]. J Math Anal Appl,1962,5:136-146.
    [13]
    LU Ting-he, SHEN Jia-qi, JIN Jun. Construction and applications of Liapunov's functions for differential equations of fourth order[J]. Journal of Shanghai Teachers University,1982,11(2).
    [14]
    QIN Yuan-xun, WANG Lian, WANG Mu-qin. Theory and Application of Motion Stability[M]. Beijing: Science Press,1981.
    [15]
    SHEN Jia-qi, LU Ting-he, JIN Jun. The construction of Liapunov's function of certain fourth order differential equations[J]. Journal of Shanghai Teachers University, 1983,12(2).
    [16]
    Yoshizawa T. Liapunov's function and boundedness of solutions[J]. Funkcialaj Ekvacioj,1959,(2).
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 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 (1980) PDF downloads(621) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return