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Pseudo asymptotically periodic solutions for Volterra integro‐differential equations
Author(s) -
Xia Zhinan
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3108
Subject(s) - mathematics , uniqueness , banach space , volterra integral equation , class (philosophy) , differential equation , mathematical analysis , function (biology) , pure mathematics , integral equation , computer science , artificial intelligence , evolutionary biology , biology
In this paper, we propose a new class of functions called pseudo S ‐asymptotically ω ‐periodic function in the Stepanov sense and explore its properties in Banach spaces including composition results. Furthermore, the existence and uniqueness of the pseudo S ‐asymptotically ω ‐periodic mild solutions to Volterra integro‐differential equations is investigated. Applications to integral equations arising in the study of heat conduction in materials with memory are shown. Copyright © 2014 John Wiley & Sons, Ltd.