Article
On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities
Author/s | Llibre Saló, Jaume
Ponce Núñez, Enrique ![]() ![]() ![]() ![]() ![]() ![]() ![]() Torres Peral, Francisco ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2008 |
Deposit Date | 2017-04-27 |
Published in |
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Abstract | In this paper we study the non-existence and the uniqueness of limit cycles for the Liénard differential equation of the form x'' − f(x)x' + g(x) = 0 where the functions f and g satisfy xf(x) > 0 and xg(x) > 0 for x ≠ 0 ... In this paper we study the non-existence and the uniqueness of limit cycles for the Liénard differential equation of the form x'' − f(x)x' + g(x) = 0 where the functions f and g satisfy xf(x) > 0 and xg(x) > 0 for x ≠ 0 but can be discontinuous at x = 0. In particular, our results allow us to prove the non-existence of limit cycles under suitable assumptions, and also prove the existence and uniqueness of a limit cycle in a class of discontinuous Liénard systems which are relevant in engineering applications. |
Citation | Llibre Saló, J., Ponce Núñez, E. y Torres Peral, F. (2008). On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities. Nonlinearity, 21 (9), 2121-2142. |
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