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.

中文翻译：

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具有非线性边界条件的肿瘤模型自由边界问题的分叉分析

在本文中，我们研究了模拟非坏死肿瘤生长的自由边界问题的非径向平稳解的存在。与现有文献中研究的有关养分浓度$ \ sigma $的边界值条件为线性的条件的模型不同，在该模型中，这是非线性的边界条件。通过使用分叉方法，我们证明了当径向张力解的表面张力系数$ \ gamma $取线性问题的某些特征值的小邻域中的值时，确实存在非径向固定解。