16th Conference on Applied Mathematics, Univ. of Central Oklahoma,
Electron. J. Diff. Eqns., Conf. 07, 2001, pp. 47-59.

### A new a priori estimate for multi-point boundary-value 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 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