Bifurcations for a multidimensional free boundary problem modeling the growth of tumor cord

This paper is devoted to studying bifurcations of a multidimensional free boundary problem modeling the growth of tumor cords. The model comprises two coupled elliptic equations defined in a bounded domain in R2R2 whose boundary is made up of two disjoint closed curves, one given and the other a priori unknown. By reducing this problem into an abstract operator equation in a certain Banach space and employing the well-known bifurcation theorem of Crandall and Rabinowitz, we prove that for the well-studied radially symmetric solution of this problem, there exists a series of numbers γkγk such that at each γkγk there exists a branch of radially non-symmetric solutions bifurcating from the radially symmetric solution.