数学物理学报 ›› 2000, Vol. 20 ›› Issue (2): 194-201.

• 论文 • 上一篇    下一篇

四阶非线性常微分方程非线性三点边值问题解的存在性与唯一性

  

  1. (北华大学师范学院数学系 吉林市 132013)
    (东北电力学院基础部 吉林市 132012)
  • 出版日期:2000-03-03 发布日期:2000-03-03

Existence and Uniqueness of Solutions of Nonlinear Three-Point Boundary Value Problems for Fourth Order Nonlinear Ordinary Differential Equations

  1. (Department of Mathematics of Normal College of Beihua University, Jilin 132013)

     

    (Department of Basic Science Courses, Northeast China Institute of Electricity Power Engineer, Jilin 132012)

  • Online:2000-03-03 Published:2000-03-03

摘要:

该文利用“Matching”技巧,给出了四阶非线性常微分方程
    y(4) = f(x, y, y′,y″,y(3)),
满足非线性三点边界条件
       k(y(b),y′(b),y″(b),y(3)(b),y(a),y′(a),y″(a),y(3)(a))=0,
       y(b)=μ
       g(y′(b),y(3)(b))=0,
       h(y(b),y′(b),y″(b),y(3)(b),y(c),y′(c),y″(c),y(3)(c))=0

的三点边值问题存在解与存在唯一解的具体的充分条件.

关键词: 四阶非线性常微分方程, 三点边值问题, 存在性, 唯一性.

Abstract:

In this paper,by using the “Matching” technique, gives concrete sufficient conditions of the existence and uniqueness of solutions of nonlinear three-point boundary value problems for fourth order nonlinear ordinary differential equation
      Y(4) = f(x, y, y′,y″,y(3)),
with the nonlinear threepoint boundary conditions
      k(y(b),y′(b),y″(b),y(3)(b),y(a),y′(a),y″(a),y(3)(a))=0,
      y(b)=μ
      g(y′(b),y(3)(b))=0,
      h(y(b),y′(b),y″(b),y(3)(b),y(c),y′(c),y″(c),y(3)(c))=0

Key words: Fourthordernonlinearordinarydifferentialequation, Threepointboundaryvalueproblems, Existence, Uniqueness.

中图分类号: 

  • 34B15