Periodic solutions of Lienard differential equations via averaging theory of order two
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 3func...
| Autor principal: | |
|---|---|
| Outros Autores: | , |
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2015
|
| Assuntos: | |
| Texto completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000501905 |
| País: | Brasil |
| Oai: | oai:scielo:S0001-37652015000501905 |
| Resumo: | 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. |
|---|