A theory for existence and uniqueness of solutions to three point boundary value problems (Q1197424)

Using Lyapunov technique the authors prove some existence and uniqueness theorems for the boundary value problem \(y^{(n)}=f(x,y,y',\ldots,y^{n-1}),\;x\in (a,b)\), \(y(a)=y_ 1\), \(y(b)=y_ 2\), and \(y^{(i)}(a)=m_ i (i=1,2,\ldots n-2)\), where the function \(f\in C([a,b]\times R^ n)\) and the constants \(y_ 1, y_ 2, m_ i\) are given.