TY - JOUR
T1 - Limit cycles for non smooth differential equations via Schwarzian derivative
AU - Coll, B.
AU - Gasull, A.
AU - Prohens, R.
PY - 1996/12/10
Y1 - 1996/12/10
N2 - We consider a class of planar polynomial systems with discontinuous righthand sides and prove that, under certain hypotheses, it presents at most one singular limit cycle and two regular limit cycles. Furthermore the sum of the multiplicity of the regular limit cycles is less or equal than two. A key point in the proof is the study of the Schwarzian derivative of the return map. Finally, we give some examples reaching these bounds. © 1996 Academic Press, Inc.
AB - We consider a class of planar polynomial systems with discontinuous righthand sides and prove that, under certain hypotheses, it presents at most one singular limit cycle and two regular limit cycles. Furthermore the sum of the multiplicity of the regular limit cycles is less or equal than two. A key point in the proof is the study of the Schwarzian derivative of the return map. Finally, we give some examples reaching these bounds. © 1996 Academic Press, Inc.
UR - https://www.scopus.com/pages/publications/0030579552
U2 - 10.1006/jdeq.1996.0177
DO - 10.1006/jdeq.1996.0177
M3 - Article
SN - 0022-0396
VL - 132
SP - 203
EP - 221
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -