Periodic solutions of Lienard differential equations via averaging theory of order two
| Autor: | JAUME LLIBRE, DOUGLAS D. NOVAES, MARCO A. TEIXEIRA |
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| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Anais da Academia Brasileira de Ciências, Vol 87, Iss 4, Pp 1905-1913 (2015) |
| Druh dokumentu: | article |
| ISSN: | 1678-2690 0001-3765 18402909 |
| DOI: | 10.1590/0001-3765201520140129 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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