Limit-periodic solutions of difference and differential systems without global lipschitzianity restrictions.

Criteria for the existence of limit-periodic solutions are established to nonlinear difference as well as differential systems governed by a Stepanov-like limit-periodic forcing. The restoring nonlinearities need not be globally Lipschitzean. The obtained sufficient conditions for difference systems are significantly more effective than those for differential systems. Nevertheless, in the continuous case, our theorems also extend some known results. A possibility of more explicit formulations are discussed in concluding remarks. [ABSTRACT FROM AUTHOR]