带有阻尼项的二阶奇异耦合系统的周期解

Periodic Solutions of the Second Order Damped Coupled Systems with Singularity

考虑耦合阻尼系统{x″+p1(t)x'+q1(t)x=f1(t,y)+e1(t),y″+p2(t)y'+q2(t)y=f2(t,x)+e2(t).周解期的存在性问题.其中pi,qi,ei∈L1(R)是T-周期函数,fi∈Car(R×R+,R)(i=1,2)在原点具有奇异性.运用Schauder不动点定理和fi的奇异性,证明该系统存在周期解.

This paper investigate the existence of periodic solntions for the damped coupled systems {x＂＋p1（t）x＇＋q1（t）x=f1（t,y）＋e1（t）,y＂＋ p2（t）y＇＋q2（t）y=f2（t,x）＋e2（t） where pi,qi,ei∈L1（R） are T - periodic, fi∈Car（R×R＋,R）（i=1,2） with the singularity at the origin. We will prove that the singularity of fi enables the existence of periodic solutions through a basic application of Schauder＇s fixed point theorem.