On S-asymptotically ω-periodic functions on Banach spaces and applications

By Hernán R. Henríquez, Michelle Pierri, P. Táboas. 2008

194 citations recorded by the source corpus.

Abstract This paper is devoted to the study of the class of continuous and bounded functions f : [ 0 , ∞ ) → X for which exists ω > 0 such that lim t → ∞ ( f ( t + ω ) − f ( t ) ) = 0 (in the sequel called S-asymptotically ω-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically ω-periodic functions. We also study the existence of S-asymptotically ω-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/1d5cc2b713a444d671f82417d1b935d48ff4ae7e

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In Applied Mathematics

In Control and Systems Engineering

Citations in the corpus

Mild solutions for abstract fractional differential equations (2013, background): “([16, 17]) A function f ∈ BC(R+, X) is called asymptotically ω-periodic for ω > 0 if there exist an ω-periodic function φ and and a h ∈ BC(R+, X) with limt→∞ h(t) = 0 such that f = φ+ h.”
Bounded Mild Solutions for Semilinear Integro Differential Equations in Banach Spaces (2010, background): “The class of functions in SAPω(X) is called S-asymptotically ω-periodic (see [27] for a discussion of qualitative properties of this class of functions).”
S‐asymptotically ω‐periodic solutions for semilinear Volterra equations (2010, background): “In particular, we extend recent results for semilinear fractional integro-difierential equations considered in [4] and for semilinear Cauchy problems of flrst order given in [ 20 ].”