Nonlinear boundary value problem, Ordinary differential equation, Nonlocal boundary condition, Boundary data smoothness
Under certain conditions, solutions of the boundary value problem y(n)=f(x,y,y′,…,y(n−1)), y(n)=f(x,y,y′,…,y(n−1)), y(i−1)(x1)=yiy(i−1)(x1)=yi for 1≤i≤n−11≤i≤n−1, and y(x2)−∑mi=1riy(ηi)=yny(x2)−∑i=1mriy(ηi)=yn, are differentiated with respect to boundary conditions, where a
Henderson, Johnny; Hopkins, Britney; Kim, Eugenie; and Lyons, Jeffrey W., "Boundary Data Smoothness for Solutions of Nonlocal Boundary Value Problems for nth Order Differential Equations" (2008). Mathematics Faculty Articles. 32.