Volume 6, Number 1, Spring 1998
SOLVABILITY OF A MULTIPOINT
BOUNDARY VALUE PROBLEM AND
RELATED A PRIORI ESTIMATES
CHAITAN P. GUPTA AND SERGEJ I. TROFIMCHUK
Abstract. Let f : [0,1] × R^{2} → R be a function
satisfying Caratheodory's conditions and e(t) ∈ L^{1} [0,1]. Let
0 < ξ_{1} < ξ_{2} < ... < ξ_{m2} < 1 and a_{i} ∈ R
for i = 1,2,...,m2, be given. This paper is concerned with the
problem of the existence of a solution for the multipoint
boundary value problem:
when all of the a_{i}'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 multipoint boundary value problem when
all of the a_{i}'s have the same sign. The results are new in case
all of the a_{i}'s do not necessarily have the same sign.
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