16th Conference on Applied Mathematics, Univ. of Central Oklahoma,
Electron. J. Diff. Eqns., Conf. 07, 2001, pp. 4759.
A new a priori estimate for multipoint boundaryvalue problem
Chaitan P. Gupta
Abstract:
Let
be a function satisfying Caratheodory's conditions and
.
Let
and
for
be given. A priori estimates of the form
are needed to obtain the existence
of a solution for the multipoint boundaryvalue problem
using Leray Schauder continuation theorem. The purpose of this
paper is to obtain a new a priori estimate of the form
.
This new estimate then enables us to obtain a new existence theorem.
Further, we obtain a new a priori estimate of the form
for the threepoint boundaryvalue problem
where
and
are given.
The estimate obtained for the threepoint boundaryvalue problem
turns out to be sharper than the one obtained by particularizing
the
point
boundary value estimate to the threepoint case.
Published July 20, 2001.
Subject lassfications: 34B10, 34B15, 34G20.
Key words: Threepoint boundaryvalue problem, $m$point boundaryvalue
problem, apriori estimates, LeraySchauder Continuation theorem,
Caratheodory's conditions.
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Chaitan P. Gupta
Department of Mathematics
University of Nevada, Reno
Reno, NV 89557 USA
email: gupta@unr.edu chaitang@hotmail.com 
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