Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations

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2020-01-01

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In this paper, we consider one-parameter ( λ>0) families of Liénard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of λ>0. To prove our main result we use the relaxation oscillation theory and a topological version of the averaging theory. More specifically, the first one is appropriate for studying the periodic solutions for large values of λ and the second one for small values of λ. In particular, our hypotheses allow us to establish a link between these two theories.

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Averaging theory, Limit cycles, Liénard equation, Relaxation oscillation theory

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Nonlinear Analysis, Theory, Methods and Applications, v. 190.

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