#### Vol. 1, No. 2, 2008

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

### Johnny Henderson, Britney Hopkins, Eugenie Kim and Jeffrey Lyons

Vol. 1 (2008), No. 2, 167–181
##### Abstract

Under certain conditions, solutions of the boundary value problem

${y}^{\left(n\right)}=f\left(x,\phantom{\rule{0.3em}{0ex}}y,{y}^{\prime },\dots ,{y}^{\left(n-1\right)}\right),$

${y}^{\left(i-1\right)}\left({x}_{1}\right)={y}_{i}$ 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}, and ${r}_{1},\dots ,{r}_{m},{y}_{1},\dots ,{y}_{n}\in ℝ$.

##### Keywords
nonlinear boundary value problem, ordinary differential equation, nonlocal boundary condition, boundary data smoothness
##### Mathematical Subject Classification 2000
Primary: 34B15, 34B10
Secondary: 34B08