一类具有时滞的Duffing型方程多重周期解的存在性

为了研究一类具有时滞的Duffing型方程的多重周期解的存在性,我们应用了推广的Poincaré-Birkhoff不动点定理.首先对一类具有时滞的Duffing型方程f给出一系列约束条件,并定义一个Poincaré映射,通过证明该映射"扭转",得出该映射在区域中至少有两个不动点,最后证明了该时滞Duffing方程f在约...

Existence of multiple periodic solutions for a class of delayed Duffing equations

The existence of multiple periodic solutions for a class of delayed Duffing-type equations was studied by using generalized Poincaré-Birkhoff fixed point theorem. Firstly, a series of constraints were added to a class of delayed Duffing-type equations f, and a Poincaré mapping was defined. By proving that the mapping was “torsional”, it was concluded that the mapping had at least two fixed points in the region. At last, the conclusion that the delayed Duffing equation f had an infinite number of periodic solutions under the constraints was proved.