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

Anais da Academia Brasileira de Ciências

Jaume Llibre¹  Douglas D. Novaes¹  Marco A. Teixeira¹ 

关键词: periodic solution;    Lienard differential equation;    averaging theory;    bifurcation theory;    solucão periódica;    equação diferencial de Lienard;    teoria da média;    teoria de bifurcação;   

DOI  :  10.1590/0001-3765201520140129

来源: SciELO

【 摘 要 】

Abstract Forε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the formx ′′ +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 aC 3function, g :ℝ → ℝis aC 4function, andp i :ℝ → ℝfori =1 , 2are continuous2 ⁢ 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.

【 授权许可】

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