Mathematics Faculty Articles

Title

Differentiation of Solutions of Nonlocal Boundary Value Problems with Respect to Boundary Data

Document Type

Article

Publication Date

7-15-2011

Publication Title

Electronic Journal of Qualitative Theory of Differential Equations

Keywords

Nonlinear boundary value problem, Variational equation, Ordinary differential equation, Nonlocal boundary condition, Uniqueness, Existence

ISSN

1417-3875

Volume

2011

Issue/No.

51

First Page

1

Last Page

11

Abstract

In this paper, we investigate boundary data smoothness for solutions of the nonlocal boundary value problem, $y^{(n)}=f(x,y,y',\ldots,y^{(n-1)}),y^{(i)}(x_j)=y_{ij}$ and $y^{(i)}(x_k)-\sum_{p=1}^m r_{ip}y(\eta_{ip})=y_{ik}.$ Essentially, we show under certain conditions that partial derivatives of the solution to the problem above exist with respect to boundary conditions and solve the associated variational equation. Lastly, we provide a corollary and nontrivial example.

Comments

Mathematics Subject Classification: 34B10, 34B15

DOI

10.14232/ejqtde.2011.1.51