Global Continua of Positive Equilibria for some Quasilinear Parabolic Equation with a Nonlocal Initial Condition

TL;DR

This paper investigates a quaslinear parabolic equation with a nonlocal initial condition, using global bifurcation theory to establish the existence of an unbounded continuum of positive solutions relevant to population dynamics.

Contribution

It introduces a novel application of global bifurcation theory to establish positive solutions for a nonlocal initial condition problem in population dynamics.

Findings

Existence of an unbounded continuum of positive solutions

Application of global bifurcation theory to nonlocal initial conditions

Relevance to nonlinear diffusion in population models

Abstract

This paper is concerned with a quaslinear parabolic equation including a nonlinear nonlocal initial condition. The problem arises as equilibrium equation in population dynamics with nonlinear diffusion. We make use of global bifurcation theory to prove existence of an unbounded continuum of positive solutions.