Chaitan P. Gupta
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: email@example.com firstname.lastname@example.org
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