Stability of solutions to a mathematical model for necrotic tumor growth with time delays in proliferation

In this paper, a mathematical model for a solid avascular tumor growth is studied. The model describes tumor growth with a necrotic core and a time delay in proliferation process. The model was proposed by Byrne and Chaplain, and was studied by M. Bodnar and U. Foryś (see [2]). Sufficient conditions which guarantee existence, uniqueness and stability of steady state are given. The results show that the dynamical behavior of the solutions of the model is similar to that of the solutions for the corresponding non-retarded problem under some assumptions. Our results partially improve the corresponding results given by M. Bodnar and U. Foryś. The results make the research for this model more perfect.