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 multi-point boundary-value 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 three-point boundary-value problem
where
and
are given.
The estimate obtained for the three-point boundary-value problem
turns out to be sharper than the one obtained by particularizing
the
-point
boundary value estimate to the three-point case.
Published July 20, 2001.
Subject lassfications: 34B10, 34B15, 34G20.
Key words: Three-point boundary-value problem, $m$-point boundary-value
problem, a-priori estimates, Leray-Schauder 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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