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

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.