Ma Ru-yun. Some Multiplicity Results for an Elastic Beam Equation at Resonance[J]. Applied Mathematics and Mechanics, 1993, 14(2): 181-188.
Citation: Ma Ru-yun. Some Multiplicity Results for an Elastic Beam Equation at Resonance[J]. Applied Mathematics and Mechanics, 1993, 14(2): 181-188.

Some Multiplicity Results for an Elastic Beam Equation at Resonance

  • Received Date: 1991-04-17
  • Publish Date: 1993-02-15
  • This paper deals with multiplicity results for nonlinear elastic equations of the type -d4u/dx44u+g(x,u)=e(x)(0R→R satisfies Carathéodory condition e∈L2[0,1].The solvability of this problem has been studied by several authors,but there isn't any multiplicity result until now to the author's knowledge.By combining the Lyapunov-Schmidt procedure with the technique of connected set,we establish several multiplicity results under suitable condition.
  • loading
  • [1]
    Reiss,E.L.,A.J.Callegari and D.S.Ahluwalia,Ordinary Differential Equations with Applicalions,Holt,Rinehart&Winston,New York(1976).
    [2]
    Usmini,R.A.,A uniqueness theorems for a boundary value problem,Proc.Amer.Math.Soc.,77,3(1979),329-335.
    [3]
    Aftabizadeh,A.R.,Existence and uniqueness theorems for fourth-order boundary value problems,J.Math.Anal.Appl.,116(1986),415-426.
    [4]
    Yang Yi-song,Fourth-order two-point boundary value problems,Proc.Amer.Math.Soc.,104,1(1988),175-180.
    [5]
    Gupta,C.P.,Existence and uniqueness theorems for the bending of an elastic beam equation,Applicable Analysis,26(1988),289-305.
    [6]
    Gupta,C.P.,Existence and uniqueness results for the bending of an elastic beam equation at resonance,J.Math.Anal.Appl.,135(1988),208-225.
    [7]
    Costa,D.G.and J.V.A.Goncalves,Existence and multiplicity results for a class of nonlinear elliptic boundary value problems at resonance,J.Math.Anal.Appl.,84,2(1981),328-337.
    [8]
    Browder,F.,Problémes Non-Linéaires,Les Presses de I'Universitéde Montreal,Montreal(1986).
    [9]
    曹之江,《常微分算子》,上海科学技术出版社(1987).
    [10]
    Mawhin,J.,J.R.Ward and M.Willem,Necessary and sufficient conditions of a nonlinear two-point boundary value problems,Proc.Amer.Math.Soc.,93(1985),667-674.
    [11]
    张石生,《不动点定理及应用》,重庆出版社(1984).
    [12]
    林宗池、林苏榕,一类向量四阶非线性微分方程边值问题的奇摄动,应用数学和力学,9(5)(1988),385-396.
  • 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 (2053) PDF downloads(586) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return