Abstract :
Let f: w0,1x=R2ªR be a function satisfying Caratheodory’s conditions and
e t.gL1w0, 1x. Let h g 0, 1., a gR, a )1, ah /1 be given. This paper is
concerned with the problem of existence of a solution for the three-point boundary
value problem
x0 t. sf t, x t., x9 t..qe t., 0-t-1,
x 0. s0, x 1. sa x h..
This problem was studied earlier by Gupta, Ntouyas, and Tsamatos when a F1
and when a )1 with ah -1. In the general case this problem was studied by
Gupta as a multi-point boundary value problem. In this paper sharper existence
conditions are obtained for the solvability of the above boundary value problem in
the general case.
