Dominant and subdominant positive solutions to generalized Dickman equation

Josef Diblík and Rigoberto Medina

Applied Mathematics and Computation, 2018, vol. 333, issue C, 169-186

Abstract: The paper considers a generalized Dickman equation tx˙(t)=−∑i=1saix(t−τi)for t → ∞ where s∈N,ai > 0, τi > 0, i=1,…,s and ∑i=1sai=1. It is proved that there are two mutually disjoint sets of positive decreasing solutions such that, for every two solutions from different sets, the limit of their ratio for t → ∞ equals 0 or ∞. The asymptotic behavior of such solutions is derived and a structure formula utilizing such solutions and describing all the solutions of a given equation is discussed. In addition, a criterion is proved giving sufficient conditions for initial functions to generate solutions falling into the first or the second set. Illustrative examples are given. Some open problems are suggested to be solved.

Keywords: Generalized Dickman equation; Positive solution; Dominant solution; Subdominant solution; Asymptotic behavior; Delay (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:333:y:2018:i:c:p:169-186

DOI: 10.1016/j.amc.2018.03.090

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