Periodic, permanent, and extinct solutions to population models

0557843 - MÚ 2023 RIV US eng J - Journal Article
Hakl, Robert - Oyarce, J.
Periodic, permanent, and extinct solutions to population models.
Journal of Mathematical Analysis and Applications. Roč. 514, č. 1 (2022), č. článku 126262. ISSN 0022-247X. E-ISSN 1096-0813
Institutional support: RVO:67985840
Keywords : boundary value problems * bounded solution * functional differential equations * periodic solution
OECD category: Pure mathematics
Impact factor: 1.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.jmaa.2022.126262

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.
Permanent Link: http://hdl.handle.net/11104/0331688