Abstract :
Let f : w0, 1x=R2ªR be continuous and egCw0, 1x. Let j ig 0, 1., aigR, all
of the ai’s having the same sign, is1, 2, . . . , my2, 0-j 1-j 2- ??? -jmy2-
1 be given. This paper is concerned with the problem of existence of a solution for
the m-point boundary value problem
x0 t . sf t , x t ., x9 t .. qe t ., tg 0, 1. E.
my2
x9 0. s0, x 1. s ai x j i .. BCm.
is1
We discuss existence theorems for the problem E.] BCm. under some sign
condition of f about the origin. Our analysis is based on a Nonlinear Alternative of
Leray-Schauder.
