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

Abstract

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.

Keywords:

• Limit-periodic functions and sequences
• semi-periodic functions and sequences
• Stepanov norm
• difference and differential systems
• exponential dichotomies
• absence of global lipschitzianity

AMS Subject Classifications:

• 34C15
• 34C27
• 34K14
• 39A10
• 42A75

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was supported by the grant IGA_PrF_2017_019 ‘Mathematical Models’ of the Internal Grant Agency of Palacký University in Olomouc.