具有偏差变元的Li\'{e}nard型方程的周期解

Periodic Solutions for a Li\'{e}nard-Type Equation with Deviating Arguments

中文关键词:  Li\'{e}nard型方程  偏差变元  周期解  重合度.

英文关键词:Li\'{e}nard-type equation  deviating arguments  periodic solution  coincidence degree.

中文摘要:

      本文利用重合度理论研究了一类具偏差变元的Li\'{e}nard型方程$$x''(t)+f_1(t,x(t))|x'(t)|^2+f_2(t,x(t),x(t-\tau_{0}(t)))x'(t)+g(t,x(t-\tau_{1} (t)))=p(t).$$获得了该方程存在$\omega$-周期解的若干新结论, 改进和推广了已有文献中的相关结果.

英文摘要:

      We use the coincidence degree theory to establish new results on the existence of $\omega$-periodic solutions for the Li\'{e}nard-type equation with deviating arguments $$x''(t)+f_1(t,x(t))|x'(t)|^2+f_2(t,x(t),x(t-\tau_{0}(t)))x'(t)+g(t,x(t-\tau_{1} (t)))=p(t).$$ The results improve and extend some existing ones in the literature.