n阶非线性微分方程边值问题解的存在唯一性

Existence-Uniqueness of Solutions of Boundary ValueProblems for Nth-Order Nonlinear Differential Equations

讨论了ｎ阶非线性微分方程ｙ（ｎ）＝ｆ（ｔ，ｙ，ｙ′，…，ｙ（ｎ－１）满足边界条件ｙ（ｎ－３）（α）＋λ０ｙ（ｎ－２）（α）＝λ１，ｙ（ｎ－１）（β）＝λｎ－１，ｙ（γ）＝λｎ，ｎ≥３，ｙ（ｊ）（β）＝λｊ＋２（ｊ＝０，１，…，ｎ－４），ｎ＞３或ｙ（ｎ－２）（α）＋λ０ｙ（ｎ－１）（α）＝λ１，ｙ（ｊ）（β）＝λｊ＋２（ｊ＝０，１，…，ｎ－３），ｙ（γ）＝λｎ的边值问题解的存在唯一性，其中α，β，γ及λｉ（ｉ＝０，１，…，ｎ）均为实数。通篇假设函数ｆ（ｔ，ｙ１，ｙ２，…，ｙｎ）是区域［α，γ］×Ｒｎ上的连续函数。

お? In this Paper,the authors discuss the existence-uniqueness of solutions of boundary value problems for nth-order nonlinear differential equation y(n)=f(t,y,y′,…,y(n-1))with boundary condition y(n-3)(α)+λ0y(n-2)(α)=λ1,y(n-1)(β)=λn-1,y(γ)=λn,n≥3,y(j)(β)=λj+2(j=0,1,…,n-4),n>3.or y(n-2)(α)+λ0y(n-1)(α)=λ1,y(j)(β)=λj+2(j=0,1,…,n-3),y(γ)=λn.where α,β,γ and λi(i=0,1,…,n) are reals,It is assumed throughout this paper that the function f(t,y1,y2,…,yn) is a continuous function on the domain×Rn.