Wu Guangrong, Huang Wenhua, Shen Zuhe. New Results of Some Existence Theorems on Nonlinear Boundary Value Problems[J]. Applied Mathematics and Mechanics, 1999, 20(1): 105-109.
Citation: Wu Guangrong, Huang Wenhua, Shen Zuhe. New Results of Some Existence Theorems on Nonlinear Boundary Value Problems[J]. Applied Mathematics and Mechanics, 1999, 20(1): 105-109.

New Results of Some Existence Theorems on Nonlinear Boundary Value Problems

  • Received Date: 1996-12-27
  • Rev Recd Date: 1998-06-18
  • Publish Date: 1999-01-15
  • With the use of the homeomorohism theory and fixed point theory, the existence and uniqueness of solutions to boundary value problems are investigated. Two basic theorems are obtained without the boundness condition, which generalizes results of Brown. When our results are applied to the existence and uniqueness of periodic solutions for nonlinear perturbed conservative systems (Newtonian equations of motion), the existence and uniqueness of the solution obtained. The results in this note seem less restrictive than those of the former papers we have seen. Mean while, as far as we know, it seems that applying the homeomorphism theory to the research of this kind of problem is new.
  • loading
  • [1]
    Brown K J.Nonlinear boundary value problems and a global inverse function theorem[J].Annali Mat Pura Appli,1975,106:205~214
    [2]
    Plastock R.Homeomorphisms between Banach spaces[J].Trans Amer Math Soc,1974,200:169~183
    [3]
    Brown K J,Lin S S.Periodically perturbed conservative system and a global inverse function theorem[J].Nonlinear Analysis,1980,TMA,4:193~201
    [4]
    Mawhin J.Recent trends in nonlinear boundary value problems[Z].In:Proc Int Conf Nonlinear Oscillations[C],Berlin:Academic-Verlag,1975:75~90
    [5]
    Bates P W.Solutions of nonlinear elliptic systems with meshed spectra[J].Nonlinear Analysis,1979,TMA,4(6):1023~1030
    [6]
    Dunford N,Schwartz J.Linear Opeator[M],volume Ⅰ,New York:Interscience,1963
    [7]
    Dunford N,Schwartz J.Linear Operator[M],Volume Ⅱ,New York:interscience,1963
    [8]
    Adams R A.Sobolev Spaces[M].New York:Academic Press,1975
    [9]
    Shen Zuhe,Wolfe M A.On the existence of periodically perturbed conservative systems[J].J Math Anal and Appl,1989,151:78~83
    [10]
    Lamberto Cesari.Optimization-Theory and Applications,Problems with Ordinary Differential Equations[M].Springer-verlag,1983.
  • 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 (1959) PDF downloads(611) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return