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

Authors

Alfredo F. Janson
Bibi T. Juman
Jeffrey W. Lyons, Nova Southeastern UniversityFollow

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