2n阶微分方程周期解的存在性

Existence of the Periodic Solution of Differential Equations of the 2nth Order

考虑微分方程u(2n)+G(u)=M(u)解的存在性问题,运用同胚理论及不动点方法给出在M为有界全连续算子条件下此类方程解的存在性定理。

For the 2nth order differential equation u^（2a）＋△↓G（u）=M（u） , under the condition of M being a bounded completely continuous operator, the existence of periodic solution is discussed by virtue of homeomorphism,and fixed point method.