The Connection between Variational Equations and Solutions of Second Order Nonlocal Integral Boundary Value Problems
Dynamic Systems and Applications
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).
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.