非线性n阶微分方程的五点边值问题解的存在唯一性(英文)  

Existence and uniqueness of solutions to nonlinear five-point boundary value problems for n-order nonlinear differential equation

作　　者：高永馨[1] 谢燕华[1] 

机构地区：[1]中国民航大学理学院,天津300300

出　　处：《黑龙江大学自然科学学报》2010年第5期582-585,共4页Journal of Natural Science of Heilongjiang University

基　　金：Supported by Civil Aviation University of China Research Foundation(05yk32s)

摘　　要：利用解的匹配方法(即将非线性微分方程y(n)=f(x,y,y′,…,y(n-1))在[x1,x3]上的三点边值问题的唯一解与在[x3,x5]上的三点边值问题的唯一解匹配,从而得到方程五点边值问题的唯一解),给出非线性n阶微分方程y(n)=f(x,y,y′,…,y(n-1))满足边界条件y(k)(x1)-y(k)(x2)=a1k,y(j)(x3)=bj+2,y(k)(x4)-y(k)(x5)=a2k,(j,k=0,1,…,n-3)的五点边值问题的解存在唯一的条件。Using the method of matching solutions（i.e.）,a solution satisfying five-point boundary conditions to the nonlinear differential equation y（n）=f（x,y,y′,…,y（n-1）） is obtained by matching its unique solution to three-point boundary value problems on with the unique solution to three-point boundary value problems on to obtain）,existence and uniqueness of solutions to five-point boundary value problems for nonlinear nth-order differential equation y（n）=f（x,y,y′,…,y（n-1））,with the boundary conditions y（k）（x1）-y（k）（x2）=a1k,y（j）（x3）=bj＋2,y（k）（x4）-y（k）（x5）=a2k,（j,k=0,1,…,n-3）.

关 键 词：非线性n阶微分方程 五点边值问题 解的存在唯一性 

分 类 号：O189.1[理学—数学]