A New Criterion for Controlling the Number of Limit Cycles of Some Generalized Liénard Equations |
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| Authors: | Armengol GasullHector Giacomini |
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| Institution: | a Dept. de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193, Bellaterra, Barcelona, Spainf1gasull@mat.uab.esf1b Laboratoire de Mathématique et Physique Théorique, CNRS (UPRES-A 6083), Faculté des Sciences et Techniques, Université de Tours, Parc de Grandmont, 37200, Tours, Francef2giacomini@univ-tours.frf2 |
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| Abstract: | We consider a class of planar differential equations which include the Liénard differential equations. By applying the Bendixson-Dulac Criterion for ?-connected sets we reduce the study of the number of limit cycles for such equations to the condition that a certain function of just one variable does not change sign. As an application, this method is used to give a sharp upper bound for the number of limit cycles of some Liénard differential equations. In particular, we present a polynomial Liénard system with exactly three limit cycles. |
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| Keywords: | ordinary differential equation limit cycle Lié nard equation |
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