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

Author(s)

Llibre, Jaume ^[1] ; Novaes, Douglas D. ^[2] ; Teixeira, Marco A. ^[2]

Affiliation

^[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[2] Univ Estadual Campinas, Dept Matemat, Rua Sergio Buarque Holanda, 651, Cidade Univ, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Anais da Academia Brasileira de Ciências; v. 87, n. 4, p. 1905-1913, DEC 2015.
• Web of Science Citations: 0

Abstract

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. (AU)

• FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/02517-6 - Study of minimal sets in nonsmooth dynamical systems
• Grantee: Douglas Duarte Novaes
• Support Opportunities: Scholarships in Brazil - Post-Doctoral