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...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000501905 |
| Country: | Brazil |
| Oai: | oai:scielo:S0001-37652015000501905 |
| Summary: | 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. |
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