摘要
用上、下解方法研究了n阶非线性微分方程k点边值问题y(n)=f(t,y(n-2),y(n-1))y(i)(di)=ai(i=0,1,…,n-3),g(y(n-2)(t1),y(n-1)(t1))=0,h(y(n-2)(tk),y(n-1)(tk))=0(1) 解的存在性、唯一性。其中tj∈R,j=1,2,…,k;t1<t2<…<tk;di∈{t1,t2,…,tk}且di取值相互独立;n≥2,2≤k≤n;g(u,v),h(u,v)是满足一定条件的二元函数。
In this paper,the author prove the existence and uniqueness of solutions for the follwing boundary value problem y<sup>(n)</sup>=f(t,y<sup>(n-2)</sup>,y<sup>(n-1)</sup>)y<sup>(i)</sup>(d<sub>i</sub>)=a<sub>i</sub>(i=0,1,...,n-3),g(y<sup>(n-2)</sup>(t<sub>1</sub>),y<sup>(n-1)</sup>(t<sub>1</sub>))=0,h(y<sup>(n-2)</sup>(t<sub>k</sub>),y<sup>(n-1)</sup>(t<sub>k</sub>))=0where t<sub>j</sub>∈R,j=1,2,...,k,t<sub>1</sub><t<sub>2</sub><...<t<sub>k</sub>,d<sub>i</sub>∈{t<sub>1</sub>,t<sub>2</sub>,...,t<sub>k</sub>}and d<sub>i</sub> is indepandent of eath other,by method of the upper and lower solutions.
出处
《沈阳教育学院学报》
2003年第4期99-102,共4页
Journal of Shenyang College of Education
关键词
非线性n阶微分方程
多点边值
上解方法
下解方法
存在性
唯一性
nth-order nonlinear differential equations
many point boundary value
existence and uniqueness
upper and lower solutions.