Solvability of a Multi-Point Boundary Value Problem at Resonance

This paper is concerned with the problem of existence of a solution for the multi-point boundary value problem, k x Žt. fŽt, xŽt., x Žt.., 0 t 1, xŽ0. 0, xŽ1. Ý ixŽ i., i 1 with Ýki 1 i i 1, in the absence of growth conditions on f. The multi-dimensional version of the problem is also considered.