## Mathematics Faculty Articles

#### Title

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.

http://nsuworks.nova.edu/math_facarticles/118