一类广义Liénard型泛函微分方程的周期解

Periodic solutions to a type of generalized Liénard functional differential equation

利用拓扑度方法研究了一类高次迭代的广义Liénard型泛函微分方程x"(t)+f(x<m>(t)) x'(f)+a(t)g(x<n>(t))十b(t)x(t)=p(t)周期解的存在性,在阻尼项f有界和无界的条件下分别讨论了方程存在周期解的充分条件.

The existence of periodic solutions for the type of generalized Lienard functional differential equations x'(t) + f(x<m>(t))x'(t) + a(t)g(x<n>(t)) + b(t)x(t) = p(t) with higher-order iteration is studied by means of the methods based on topological degree theory, and on conditions that f is bounded or unbounded, sufficient condition for the equation with periodic solutions is obtained respectively.