1,839 research outputs found
Global Bifurcation of Positive Equilibria in Nonlinear Population Models
Existence of nontrivial nonnegative equilibrium solutions for age structured
population models with nonlinear diffusion is investigated. Introducing a
parameter measuring the intensity of the fertility, global bifurcation is shown
of a branch of positive equilibrium solutions emanating from the trivial
equilibrium. Moreover, for the parameter-independent model we establish
existence of positive equilibria by means of a fixed point theorem for conical
shells.Comment: 17 page
On Positive Solutions of Some System of Reaction-Diffusion Equations with Nonlocal Initial Conditions
The paper focuses on positive solutions to a coupled system of parabolic
equations with nonlocal initial conditions. Such equations arise as
steady-state equations in an age-structured predator-prey model with diffusion.
By using global bifurcation techniques, we describe the structure of the set of
positive solutions with respect to two parameters measuring the intensities of
the fertility of the species. In particular, we establish co-existence
steady-states, i.e. solutions which are nonnegative and nontrivial in both
components
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