一类n阶非线性微分方程多点边值问题解的存在性  

Existence of Solutions of Multy-Point Boundary Value Problems for A Class of n-th-Order Nonlinear Differential Equations

作　　者：邬伟三[1] 张淑艳[1] 

机构地区：[1]白城师范学院数学系,吉林白城137000

出　　处：《白城师范学院学报》2009年第3期8-12,共5页Journal of Baicheng Normal University

摘　　要：利用Leray-Schauder度理论建立了n阶非线性微分方程y(n)=f(x,y,y′,…,y(n-1)),n≥3,满足多点边界条件yn-1(0)-hyn-2(0)=0,y(i)(ηi)=0,i=0,1,…,n-3,y(n-1)(1)+ky(n-2)(1)=0.的多点边值问题的解存在性的几个充分条件,并给出了应用举例.In this paper,we apply the Leray-Schauder degree theory to obtain some sufficient conditions of the existence of solution of multy-point boundary value problem for n-th order nonlinear differential equationsy(n)=f(x,y,y′,…,y(n-1)),n≥3,with the boundary conditionsyn-1(0)-hyn-2(0)=0,y(i)(ηi)=0,i=0,1,…,n-3,y(n-1)(1)+ky(n-2)(1)=0and then we give some examples of the applications in our results.

关 键 词：n阶非线性微分方程 多点边值问题 存在性 

分 类 号：O175.8[理学—数学]