We deal with the nonlinear impulsive periodic boundary value
problem $u''= f(t,u,u')$ , $u(t_i+)=\mathrm{J}_i(u(t_i))$ , $u'(t_i+)=\mathrm{M}_i(u'(t_i))$ , $i=1,2,\dotsc,m$ , $u(0)=u(T)$ , $u'(0)= u'(T)$ . We establish the existence results which rely on
the presence of a well-ordered pair $(\sigma_1,\sigma_2)$ of
lower/upper functions $(\sigma_1\le\sigma_2 \text{ on } [0,T])$ associated with the problem. In contrast to previous papers
investigating such problems, the monotonicity of the impulse
functions $\mathrm{J}_i$ , $\mathrm{M}_i$ is not required here.