Existence of periodic solutions for p(t)p(t)-Laplacian systems

In this paper, by using minimax methods in critical point theory, we obtain some existence theorems for periodic solutions of p(t)p(t)-Laplacian system {(|u′(t)|p(t)−2u′(t))′+∇F(t,u(t))=0,u(0)−u(T)=u′(0)−u′(T)=0 and our results generalize some existed theorems.