Periodic solutions for n-dimensional generalized Liénard type p-Laplacian functional differential system

We consider the n-dimensional generalized Liénard system frac(d, d t) φ{symbol}p[(x (t) - C x (t - τ))′] + frac(d, d t) ∇ F (x (t - τ)) + ∇ G (x (t - δ (t))) = e (t) driven by the scalar p-Laplacian, C is an n × n symmetric matrix of constants. Using the degree theory, we establish some criteria to guarantee the existence of periodic solutions for the above system, which generalize and improve on the corresponding results in the related literature.