Periodic solutions for 2kth boundary value problem with resonance

In this paper, a non-variational version of a max–min principle is extended, and some unique existence results for the periodic boundary value problem of the higher order nonconservative systems with resonance u(2k)(t) + k j=1 Aj u(2j−1)(t) + (−1)k−1∇G(u, t) = e(t) are obtained.  2005 Elsevier Inc. All rights reserved.