Periodic solutions for second order equations with time-dependent potential via time map ✩

In this paper the approach via time-map is used to investigate the existence of periodic solutions for second order equation with time-dependent potential. Our theorem generalized the results obtained by Ding, Habets, Omari and Zanolin which are for time-independent potential and relate the behavior of the primitive of the nonlinearity with respect to the Fuˇcik spectrum of the periodic problem.  2004 Elsevier Inc. All rights reserved.