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

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.