非线性四阶常微分方程三点边值问题解的存在性

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Existence of Solutions of Three-Point Boundary Value Problems for Nonlinear Fourth order Differential Equation

Department of Basic Science, Northeast Institute of Electric Power, Jilin 132012, P. R. China

摘要: 本文利用文献[1]、[2]的方法,讨论了非线性四阶常微分方程满足如下条件的三点边值问题解的存在性。对于非线性四阶常微子方程的边值问题,到目前已经有了一系列的研究。而本文所讨论的方程(*),具非线性边界条件(**)的边值问题解的存在性,则是上述工作未曾涉及的。本文主要定理的推论,方程(*)之具如下形式的边界条件的边值问题解的存在性,以前的工作也未涉及。
- 非线性四阶微分方程 /
- 三点边值问题 /
- 解的存在性
Abstract: In this paper.the author uses the methods in [1,2] to study the existence of solutions of three point boundary value problems for nonlinear fourth order differential equation.
- nonlinear fourth order differential equation /
- three-point boundary value problems /
- existence of solutions

[1]	G. A. Klasen, Differential inequalities and existence theorems for second and third order boundary value problems, J. Differential Equation. 10(1971),529-537.
[2]	Wang Zin zi, Existence of solutions of nonlinear two-point boundary value problems for third order nonlinear differential equations, Nonlinear differential equations, Northeast Math, J., 7, 2(1991), 181-189.
[3]	L. K. Jackson and K.Schrader, Subfunction and Third order differential inequalities, J. Differential Equation, 8(1970), 180-194.
[4]	P. Hartman, Ordinary Differential Equations, Wiley, New York(1964).
[5]	Zhao Weili, Existence of solutions of boundary value problems for third order nonlinear differential equations, Acta Scientiarum Naturalium Universitatis Jilinensis, 2(1984),10-19.