Jeffrey W. Lyons, Samantha A. Major and Kaitlyn B.
Seabrook
Vol. 11 (2018), No. 1, 95–102
DOI: 10.2140/involve.2018.11.95
Abstract
Using a few conditions, continuous dependence, and a result regarding smoothness of
initial conditions, we show that derivatives of solutions to the second order boundary value
problem
,
, satisfying
,
, where
and
with respect to each
of the boundary data
,
,
,
,
solve
the associated variational equation with interesting boundary conditions. Of note is
the second boundary condition, which is an average value condition.
Keywords
continuous dependence, boundary data smoothness, average
value condition, Peano's theorem