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Weighted Sp-pseudo S-asymptotic periodicity and applications to Volterra integral equations

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  • He, Bing
  • Wang, Qi-Ru
  • Cao, Jun-Fei

Abstract

This paper is related to the function space formed by weighted Sp-pseudo S-asymptotic periodicity and their applications. Initially, the translation invariance and completeness of the function space are investigated. Additionally, the composition theorem and convolution operator generated by Lebesgue integrable functions are presented. Finally, existence and uniqueness of solutions with weighted Sp-pseudo S-asymptotic periodicity for two classes of Volterra equations are proved by using the results obtained above, and some concrete examples are given. The methods mainly include Minkowski’s inequality, convolution inequality, contraction mapping principle, and especially the generalized Minkowski’s inequality. Our results extend some known results on asymptotic periodicity.

Suggested Citation

  • He, Bing & Wang, Qi-Ru & Cao, Jun-Fei, 2020. "Weighted Sp-pseudo S-asymptotic periodicity and applications to Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    • Handle: RePEc:eee:apmaco:v:380:y:2020:i:c:s0096300320302447
    DOI: 10.1016/j.amc.2020.125275
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    References listed on IDEAS

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    1. Henríquez, Hernán R. & Pierri, Michelle & Rolnik, Vanessa, 2016. "Pseudo S-asymptotically periodic solutions of second-order abstract Cauchy problems," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 590-603.
    2. Shu, Xiao-Bao & Xu, Fei & Shi, Yajing, 2015. "S-asymptotically ω-positive periodic solutions for a class of neutral fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 768-776.
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