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)

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。

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

Using the method of matching solutions (i. e.), a solution satisfying five - point bounda-unique solution to three- point boundary value problems on x1,x3]with the unique solution to three-point boundary value problems on x3,x5]to obtain), existence and uniqueness of solutions to five -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).