(ω, c)‐asymptotically periodic functions, first‐order Cauchy problem, and Lasota‐Wazewska model with unbounded oscillating production of red cells. (16th September 2019)

• Record Type: Journal Article
• Authors: Alvarez, Edgardo; Castillo, Samuel; Pinto, Manuel
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 1(2020)
• Page Start: 305
• Page End: 319
• Publication Date: 2019-09-16
• Subjects: antiperiodic -- completeness -- convolution invariance -- periodic -- (ω;c)‐periodic; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5880
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we study a new class of functions, which we call ( ω, c )‐asymptotically periodic functions. This collection includes asymptotically periodic, asymptotically antiperiodic, asymptotically Bloch‐periodic, and unbounded functions. We prove that the set conformed by these functions is a Banach space with a suitable norm. Furthermore, we show several properties of this class of functions as the convolution invariance. We present some examples and a composition result. As an application, we prove the existence and uniqueness of ( ω, c )‐asymptotically periodic mild solutions to the first‐order abstract Cauchy problem on the real line. Also, we establish some sufficient conditions for the existence of positive ( ω, c )‐asymptotically periodic solutions to the Lasota‐Wazewska equation with unbounded oscillating production of red cells.