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

Abstract

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．

CLC Number:

３４Ｂ１５

Pei Minghe Yu Hailan. Existence and Uniqueness of Solutions of Nonlinear Three-Point Boundary Value Problems for Fourth Order Nonlinear Ordinary Differential Equations[J].Acta mathematica scientia,Series A, 2000, 20(2): 194-201.

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References

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８　高永馨．非线性四阶常微分方程三点边值问题解的存在性．应用数学和力学，１９９６，１７：５４３－５５０
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１０　ＨａｒｔｍａｎＰ．ＯｒｄｉｎａｒｙＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓ．ＮｅｗＹｏｒｋ：Ｗｉｌｅｙ，１９６４

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

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