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Periodic, permanent, and extinct solutions to population models
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SYSNO ASEP 0557843 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Periodic, permanent, and extinct solutions to population models Author(s) Hakl, Robert (MU-W) RID, SAI, ORCID
Oyarce, J. (CL)Article number 126262 Source Title Journal of Mathematical Analysis and Applications. - : Elsevier - ISSN 0022-247X
Roč. 514, č. 1 (2022)Number of pages 60 s. Language eng - English Country US - United States Keywords boundary value problems ; bounded solution ; functional differential equations ; periodic solution Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000832060500013 EID SCOPUS 85129037679 DOI 10.1016/j.jmaa.2022.126262 Annotation The existence of a critical parameter λc>0 is proven for some population models, that splits the set of parameters into two parts where the existence, resp. nonexistence, of a positive periodic solution is guaranteed. Moreover, it is shown that in a quite wide class of population models, all the positive solutions are permanent, resp. extinct ones, provided there exists, resp. does not exist, a positive periodic solution. The results are based on a theoretical research dealing with a boundary value problem for functional differential equation with a real parameter u′(t)=ℓ(u)(t)+λF(u)(t)for a.e. t∈[a,b],h(u)=0, where ℓ and F:C([a,b],R)→L([a,b],R) are, respectively, linear and nonlinear operators, h:C([a,b],R)→R is a linear functional, and λ∈R is a real parameter. The results are illustrated by numerical simulations. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2023 Electronic address https://doi.org/10.1016/j.jmaa.2022.126262
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