Periodic solutions of Lienard differential equations via averaging theory of order two - LLIBRE,JAUME (2015)
Abstract For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x ′′ + f ⁢ ( x ) ⁢ x ′ + n 2 ⁢ x + g ⁢ ( x ) = ε 2 ⁢ p 1 ⁢ ( t ) + ε 3 ⁢ p 2 ⁢ ( t ) , where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C 4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 ⁢ π–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.