The existence of periodic solution and asymptotic behavior of solutions for a multi-layer tumor model with a periodic provision of external nutrients

Abstract

In this paper, we consider a multi-layer tumor model with a periodic provision of external nutrients. The domain occupied by tumor has a different shape (flat shape) than spherical shape which has been studied widely. The important parameters are periodic external nutrients Φ(t) and threshold concentration for proliferation σ. In this paper, we give a complete classification about Φ(t) and σ according to global stability of zero equilibrium solution or global stability of the positive periodic solution. Precisely, if 1then the zero equilibrium solution is globally stable while if 1 T T 0 Φ(t)dt > σ, then there exists a unique positive T-periodic solution and it is globally stable.