## Mathematics Faculty Articles

# The Connection between Variational Equations and Solutions of Second Order Nonlocal Integral Boundary Value Problems

## Document Type

Article

## Publication Date

6-1-2014

## Publication Title

Dynamic Systems and Applications

## ISSN

1056-2176

## Volume

23

## Issue/No.

2

## First Page

493

## Last Page

503

## Abstract

In this paper, we make certain continuity and disconjugacy assumptions upon the second order boundary value problem with nonlocal integral boundary conditions, y '' = f (x, y, y'), Y(x(1)) = y(1), and y(x(2)) + integral(d)(c) ry(x)dx, a < x(1) < c < d < x(2) < b, y(1), y(2), r is an element of R. Then, supposing we have a solution, y(x), of the boundary value problem, we differentiate the solution with respect to various boundary parameters. We show that the resulting function solves the associated variational equation of y(x).

## NSUWorks Citation

Janson, Alfredo F.; Juman, Bibi T.; and Lyons, Jeffrey W., "The Connection between Variational Equations and Solutions of Second Order Nonlocal Integral Boundary Value Problems" (2014). *Mathematics Faculty Articles*. 117.

https://nsuworks.nova.edu/math_facarticles/117