Positive solutions of a system arising from angiogenesis

Abstract

We study a system of equations arising from angiogenesis which contains a nonregular term that vanishes below a certain threshold. This loss of regularity forces one to modify the usual methods of bifurcation theory. Nevertheless, we obtain results on the existence, uniqueness and permanence of a positive solution for the time-dependent problem; and the existence and uniqueness of a positive solution for the stationary one.