Weighted pseudo asymptotically antiperiodic sequential solutions to semilinear difference equations

Abstract

In this paper, we firstly introduce the notion of weighted pseudo S-asymptotically ω-antiperiodic sequence and prove some fundamental properties of such sequences. Then we investigate some existence results for weighted pseudo S-asymptotically ω-antiperiodic solutions to a semilinear difference equation of convolution type. We establish some existence and uniqueness of weighted pseudo S-asymptotically ω-antiperiodic sequential solutions under the global Lipschitz growth condition on the second variable of the force term with different Lipschitz coefficients such as a constant, a summable function and a qth summable function, respectively. Particularly with an appropriate selection of a weight, one of our results shows that the strict contraction on the norm of Lipschitz coefficients is not necessarily required for the existence and uniqueness of weighted pseudo S-asymptotically ω-antiperiodic sequential solutions. We also prove some existence results for weighted pseudo S-asymptotically ω-antiperiodic sequential solutions under a local Lipschitz or a non-Lipschitz growth condition on the second variable of the force term, respectively.

Keywords:

• Weighted pseudo S-asymptotically ω-antiperiodic sequences
• difference equations
• existence and uniqueness

Mathematics Subject Classification (2020):

• 39A23
• 39A24
• 34G20

Acknowledgements

Authors would like to thank the anonymous referee for carefully reading this manuscript and giving valuable suggestion to improve this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NSF of Shaanxi Province (2020JM-183).