迭代微分方程“非汉字字符”+g(x(x))=p(t)的周期解

Periodic Solutions for the Differential-Iterative Equation “非汉字符号”+g(x(x))=p(t)

研究二阶迭代微分方程 x+g(x(x) ) =p(t) T-周期解的存在性 ,其中 g,p均连续 ,p(t+T) =p(t) ,且∫T0p (t) dt=0 .主要方法是先估计解的先验界 ,再用 Mawhin连续性定理得出周期解的存在性 .在对 g要求更宽松的条件下 ,得到了方程 T-周期解存在的充分条件 .

The existence of T-periodic solutions for the second order differential-iterative equation +g(x(x))=p(t) is studied, where g and p are continuous, p(t+T)=p(t),∫ T 0p(t)dt=0. A priori bounds are established for periodic solutions of the equation. By means of these bounds, an existence theorem for periodic solutions can be obtained by means of Mawhin's continuation theorem. The results are proved under better conditions of g.