Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 195, pp. 18.
Limit cycles for discontinuous generalized Lienard
polynomial differential equations
Jaume Llibre, Ana Cristina Mereu
Abstract:
We divide
into sectors
,
with
even,
and define a discontinuous differential system such that in each sector,
we have a smooth generalized Lienard polynomial differential equation
,
alternatively, where
and
are polynomials of degree n1 and m respectively.
Then we apply the averaging theory for firstorder discontinuous differential
systems to show that for any
and
there are nonsmooth Lienard polynomial
equations having at least max{n,m} limit cycles.
Note that this number is independent of the number of sectors.
Submitted May 7, 2013. Published September 3, 2013.
Math Subject Classifications: 34C29, 34C25, 47H11.
Key Words: Limit cycles; nonsmooth Lienard systems; averaging theory.
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Jaume Llibre
Departament de Matematiques
Universitat Autonoma de Barcelona
08193 Bellaterra, Barcelona, Catalonia, Spain
email: jllibre@mat.uab.cat


Ana Cristina Mereu
Department of Physics, Chemistry and Mathematics
UFSCar 18052780, Sorocaba, SP, Brazil
email: anamereu@ufscar.br

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