Uniqueness of limit cycles for Lienard differential equations of degree four

作者：Li Chengzhi^*; Llibre Jaume

来源：Journal of Differential Equations, 2012, 252(4): 3142-3162.

DOI：10.1016/j.jde.2011.11.002

• Lienard equations
• Limit cycle

We prove that any classical Lienard differential equation of degree four has at most one limit cycle, and the limit cycle is hyperbolic if it exists. This result gives a positive answer to the conjecture by A. Lins, W. de Melo and CC. Pugh (1977) [4] about the number of limit cycles for polynomial Lienard differential equations for n = 4.

• 出版日期2012-2-15
• 单位北京大学