| Abstract: | In this paper, we consider a free boundary tumor model with a periodic supply of external nutrients, so that the nutrient concentration σ satisfies σ = ?(t) on the boundary, where ?(t) is a positive periodic function with period T. A parameter μ in the model is proportional to the “aggressiveness” of the tumor. If  , where  is a threshold concentration for proliferation, Bai and Xu Pac J Appl Math. 2013;5;217‐223] proved that there exists a unique radially symmetric T‐periodic positive solution (σ?(r,t),p?(r,t),R?(t)), which is stable for any μ > 0 with respect to all radially symmetric perturbations. 17 We prove that under nonradially symmetric perturbations, there exists a number μ? such that if 0 < μ < μ?, then the T‐periodic solution is linearly stable, whereas if μ > μ?, then the T‐periodic solution is linearly unstable. |
