一类高阶微分方程周期解的存在唯一性

The Existence and Uniqueness of Periodic Solution to a 2k Higher Order Differential Equation

通过引入非负强制函数,利用全局同胚理论证明了2k阶微分方程k∑j=1jαu(2j)(t)+(-1)k+1f(x,u(t))=0(x∈Rn,aj是常数)周期解存在的充分条件,证明定理1是定理3的推论。

By the introduction of nonnegative auxiliary scalar coercive function,and the use of a global inverse theorem,this paper proves the sufficient condition of the existence 2k（∑kj=1αju（2j）（t）＋（-1）k＋1f（x,u（t））=0） periodic solution and proves that theorem 1 is the inference of theorem 3.