BIFURCATION ANALYSIS OF A TUMOR-MODEL FREE BOUNDARY PROBLEM WITH A NONLINEAR BOUNDARY CONDITION

In this paper we study existence of nonradial stationary solutions of a free boundary problem modeling the growth of nonnecrotic tumors. Unlike the models studied in existing literatures on this topic where boundary value condition for the nutrient concentration sigma is linear, in this model this is a nonlinear boundary condition. By using the bifurcation method, we prove that nonradial stationary solutions do exist when the surface tension coefficient gamma takes values in small neighborhoods of certain eigenvalues of the linearized problem at the radial stationary solution.