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.