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This article is available for purchase or by subscription. See below.
Abstract
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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.
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Keywords
continuous dependence, boundary data smoothness, average
value condition, Peano's theorem
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Mathematical Subject Classification 2010
Primary: 34B10
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Milestones
Received: 3 August 2016
Revised: 13 August 2016
Accepted: 28 August 2016
Published: 17 July 2017
Communicated by Martin J. Bohner
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