一类高维Liёnard型系统周期解的存在性

Existence of periodic solutions for a class Liёnard type system in R^N

利用重合度理论中的新Borsuk定理,得到了高维Liёnard型系统u″(t)+ddt F(u(t))+G(u(t))=e(t)存在周期解的充分条件.将线性变换引入先验估计,把F和G要求的非退化特征推广到了具有一定退化性质的情形.

Using the generalized Borsuk theorem from coincidence degree theory, some sufficient conditions for the existence of a Liёnard type system in R^N of the form u″（t）＋d/dt △↓F（u（t））＋△↓（u（t））=e（t） were proposed. By introducing linear transformation into the a priori estimation, the non-degeneration characteristics required by F and G were generalized in order to be degenerated.