Solutions of two-point BVPs at resonance for higher order impulsive differential equations

In this paper, the resonance two-point boundary value problems for impulsive 2n-order differential equation [GRAPHICS] with following two-point boundary value conditions X((2i+1)) (0) = X((2i+1)) (1) = 0, i = 0..... n - 1, and for n-order differential equation [GRAPHICS] with following periodic boundary value conditions x((i))(0) = x((i))(1), i = 0, . . . , n - 1 are considered. Sufficient conditions which guarantee the existence of at least one solution for these problems are established. The interest is that we allow the degree of variables of f to be greater than 1. The methods used and results obtained are new and they shows us that the solvability of these two problems are very much alike. (C) 2004 Published by Elsevier Ltd.