中文摘要：

研究具有抑制物因子的肿瘤生长模型的自由边界问题,主要分析该问题的分歧现象.此模型中肿瘤的进攻性由参数μ来描述,首先证明了该问题当半径r=Rs时有唯一径向对称稳态解.在此基础上还证明了存在正整数m＊＊∈R和序列μ_m,使得μ_m（m〉m＊＊）,均存在由径向对称稳态解分歧出来的非径向对称稳态解.

英文摘要：

A free boundary problem modeling tumor growth with inhibitors is considered,and the bifurcation phenomenon of the problem is mainly analyzed. The aggressiveness is modeled by a positive tumor aggressiveness parameter μ. Firstly,it is proved that this problem has a unique radially symmetric stationary solution with radius r =Rs. On this basis,it is also shown that there exist a positive integer m＊＊∈ R and a sequence of μm,such that for each μ_m（ m 〉m＊＊）,symmetric-breaking solutions bifurcate from the radially symmetric stationary solutions.