Speaker: Robert Halk
Institución: Institute of Mathematics, Brno Branch Czech Academy of Sciences.
Titulo: “Positive Solutions to Boundary Value Problems for Functional Differential Equations”
Fecha: Jueves 21 de enero 2021
Horario: 16:30 a 17:30 hrs.
Lugar: Conferencia Online.
Consider an equation
u'(t) = l(u)(t) + λF(u)(t), for a.e. t ∈ [a, b]. (1)
subject to a boundary condition
h(u) = 0. (2)
Here l : C([a, b]; R) → L([a, b], R) and h : C([a, b]; R) → R are linear bounded operators, F : C([a, b]; R) → L([a, b]; R) is a continuous operator satisfying Carathéodory conditions, and λ ∈ R is a parameter. We establish sufficient conditions guaranteeing the existence of positive solutions to (1), (2). Then we study different properties of these solutions with respect to the parameter λ. Finally, the obtained results are applied to some population models.