一类自变数镜射微分方程伪概周期解的存在性

Existence of pseudo almost periodic solutions for a class differentional equations reflection of argument

设f:R×R×R→R的连续函数.在f是伪概周期函数的前提下研究自变数镜射微分方程.x(t)+ax(t)+bx(-t)=f(t,x(t),x(-t)),b≠0,t∈R.伪概周期解的存在惟一性.研究工具是压缩映射原理.

Let f∈C（R×R×R,R）. Under pseudo almost periodic function condition on the nonlinearity f ,it is investigated that the existence of pseudo almost periodic solutions for differentional equations with reflection of the argument x（t）＋ax（t）＋bx（-t）=f（t,x（t）,x（-t））,b≠0,t∈R.The analysis is based on the banach contraction mapping theory.