Periodic solutions of Lienard differential equations via averaging theory of order two.

For ε ≠ 0 sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x'' + f ⁢(x)⁢ x' + n2⁢x + g (x) = ε2p1 ⁢(t) + ε3 ⁢p2(t), where n is a positive integer, f : ℝ → ℝ is a C 3 function, g : ℝ → ℝ is a C 4 function, and p i : ℝ → ℝ for i = 1, 2 are continuous 2π-periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.