Mathematics Faculty Articles
The Derivative of a Solution to a Second Order Parameter Dependent Boundary Value Problem with a Nonlocal Integral Boundary Condition
Document Type
Article
Publication Date
9-1-2015
Publication Title
Journal of Mathematics and Statistical Science
ISSN
2411-2518
Volume
2015
Issue/No.
2
First Page
43
Last Page
50
Abstract
We discuss derivatives of the solution of the second order parameter dependent boundary value problem with an integral boundary condition y”=f(x,y,y′,λ),y(x1)=y1,y(x2)+∫dcry(x)dx=y2 y”=f(x,y,y′,λ),y(x1)=y1,y(x2)+∫cdry(x)dx=y2 and its relationship to a second order nonhomogeneous differential equation which corresponds to the traditional variational equation. Specifically, we show that given a solution y(x) of the boundary value problem, the derivative of the solution with respect to the parameter λ is itself a solution to the aforementioned nonhomogeneous equation with interesting boundary conditions.
NSUWorks Citation
Lyons, Jeffrey W. and Miller, Joseph K., "The Derivative of a Solution to a Second Order Parameter Dependent Boundary Value Problem with a Nonlocal Integral Boundary Condition" (2015). Mathematics Faculty Articles. 118.
https://nsuworks.nova.edu/math_facarticles/118
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