Mathematics Faculty Articles
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.
NSUWorks Citation
Lyons, Jeffrey W., "Differentiation of Solutions of Nonlocal Boundary Value Problems with Respect to Boundary Data" (2011). Mathematics Faculty Articles. 50.
https://nsuworks.nova.edu/math_facarticles/50
DOI
10.14232/ejqtde.2011.1.51
COinS
Comments
Mathematics Subject Classification: 34B10, 34B15