Boundary data smoothness for solutions of nonlocal boundary value problems for $n$-th order differential equations

Abstract

Under certain conditions, solutions of the boundary value problem

$$y^{\left(n\right)}=f\left(x,y,y^{\prime },\dots ,y^{\left(n-1\right)}\right),$$

$y^{\left(i-1\right)}\left(x_1\right)=y_i$ for $1\le i\le n-1$, and $y\left(x_2\right)-{\sum }_{i=1}^m{r}_{i}y\left({\eta }_i\right)=y_n$, are differentiated with respect to boundary conditions, where $a<x_1<{\eta }_1<\cdots <{\eta }_m<x_2<b$, and $r_1,\dots ,r_m,y_1,\dots ,y_n\in ℝ$.