Anti-periodic solutions for a gradient system with resonance via a variational approach

In this paper, we investigate a second-order resonance anti-periodic boundary value problem {q(t) + lambda(m) q(t) + del F (t,q(t)) = 0, t is an element of vertical bar 0,T vertical bar, q(0) = -q(T), q(0) = -q(T), where lambda(m) is the m-th eigenvalue of the corresponding eigenvalue problem. By using the dual least action principle, we obtain an existence result. In addition, we obtain the existence of 2T-periodic solutions for q(t) + lambda(m) q(t) + del F(t, q(t)) = 0, t. R. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim