Solutions of the Variational Equation for an n-th Order Boundary Value Problem with an Integral Boundary Condition
We discuss differentiation of solutions to the boundary value problem
y(n) = ƒ (x, y, y′, y′′, …, y(n−1) ), α < x < b,
y(i) (xj) = yij, 0 ≤ i ≤ mj, 1 ≤ j ≤ k − 1,
y(i) (xk) + ∫ d c py(x) dx=yik, 0 ≤ i ≤ mk, ∑k i=1 mi = n,
with respect to the boundary data. We show that under certain conditions, partial derivatives of the solution y(x) of the boundary value problem with respect to the various boundary data exist and solve the associated variational equation along y(x).
Mathematical Sciences Publishers
Jeffers, B. L., & Lyons, J. W. (2021). Solutions of the variational equation for an n-th order boundary value problem with an integral boundary condition. Involve, 14(1), 155-166. http://doi.org/10.2140/INVOLVE.2021.14.155