Title

Solutions of the Variational Equation for an n-th Order Boundary Value Problem with an Integral Boundary Condition

Document Type

Article

Publication Date

2021

Abstract

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).

Identifier

85102875844 (Scopus)

DOI

10.2140/INVOLVE.2021.14.155

Publisher

Mathematical Sciences Publishers

ISSN

19444176

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