On second order periodic boundary-value problems with upper and lower solutions in the reversed order

In this paper, we study the differential equation with the periodic boundary value $$displaylines{ u''(t)=f(t, u(t), u'(t)),quad tin [0, 2pi]cr u(0)=u(2pi), quad u'(0)=u'(2pi). }$$ The existence of solutions to the periodic boundary problem above with appropriate conditions is proved by using an upper and lower solution method.