Pseudo Asymptotically Periodic Solutions for Volterra Difference Equations of Convolution Type
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In this paper, the author studies the existence and uniqueness of discrete pseudo asymptotically periodic solutions for nonlinear Volterra difference equations of convolution type, where the nonlinear perturbation is considered as Lipschitz condition or non-Lipschitz case, respectively. The results are a consequence of application of different fixed point theorems, namely, the contraction mapping principle, the Leray-Schauder alternative theorem and Matkowski’s fixed point technique.
KeywordsPseudo asymptotically periodic function Volterra difference equations Contraction mapping principle Leray-Schauder alternative theorem
2000 MR Subject Classification65Q10 35B40
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The author would like to thank the anonymous referees for their careful reading of the manuscript and numerous suggestions for its improvement.
- Chen, X. and Du, Z. J., Existence of positive periodic solutions for a neutral delay predator-prey model with Hassell-Varley type functional response and impulse, Qual. Theory Dyn. Syst., 2017, DOI: https://doi.org/10.1007/s12346-017-0223-6.