非线性4n阶常微分方程三点边值问题解的存在性

Existence of Solutions of Three-Point Boundary Value Problems for 4Nth-order Nonlinear Differential Equation

利用文献 [1]、[2 ]的方法 ,讨论了非线性 4n阶常微分方程y( 4n) =f(t ,y ,y′ ,y″ ,… ,y( 4n-1) ) ( )满足如下条件y( 2i+ 1) (a) =a2i+ 1,y( 2i) (c) =c2i(i=0 ,1,… ,2n- 3) ,y( 4n-2 ) (a) =a4n-2 ,y( 4n-4) (b) =b4n-4,y( 4n-3 ) (b) =b4n-3 ,y( 4n-2 ) (c) =c4n-2的三点边值问题解的存在性 ,其中函数 f是具有一定单调性质的连续函数。

In this paper,the author uses the methods in ,to study the existence of solutions of three point boundary value problems for nonlinear 4nth- order differential equation y (4n) =f(t,y,y′,y″,...,y (4n-1) )() with the boundary conditions y (2i+1) (a)=a 2i+1 ,y (2i) (c)=c 2i (i=0,1,...,2n-3),y (4n-2) (a)=a 4n-2 , y (4n-4) (b)=b 4n-4 ,y (4n-3) (b)=b 4n-3 ,y (4n-2) (c)=c 4n-2 where function f is continuous with certain monotone conditions.