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 resonanceu(2k)(t)+∑j=1kAju(2j−1)(t)+(−1)k−1∇G(u,t)=e(t) are obtained.