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Volume 6,     Number 1,     Spring 1998

 

SOLVABILITY OF A MULTI-POINT
BOUNDARY VALUE PROBLEM AND
RELATED A PRIORI ESTIMATES
CHAITAN P. GUPTA AND SERGEJ I. TROFIMCHUK

Abstract. Let f : [0,1] × R2R be a function satisfying Caratheodory's conditions and e(t)L1 [0,1]. Let 0 < ξ1 < ξ2 < ... < ξm-2 < 1 and aiR for i = 1,2,...,m-2, be given. This paper is concerned with the problem of the existence of a solution for the multi-point boundary value problem:

when all of the ai's do not necessarily have the same sign. A priori estimates of Poincaré type are obtained for , norms of the functions x(t) and x'(t) . These give sharper solvability conditions for the multi-point boundary value problem when all of the ai's have the same sign. The results are new in case all of the ai's do not necessarily have the same sign.

 

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