Existence Theorems for a Second Order m-Point Boundary Value Problem

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.