Bifurcation for a free boundary problem modeling the growth of multi-layer tumors

In this paper we study bifurcations for a free boundary problem modeling the growth of multi-layer tumors under the action of inhibitors. An important feature of this problem is that the surface tension effect of the free boundary is taken into account. By reducing this problem into an abstract bifurcation equation in a Banach space, overcoming some technical difficulties and finally using the Crandall–Rabinowitz bifurcation theorem, we prove that this problem has infinitely many branches of bifurcation solutions bifurcating from the flat solution.