American Institute of Mathematical Sciences

June  2018, 23(4): 1767-1795. doi: 10.3934/dcdsb.2018083

Nonlocal elliptic system arising from the growth of cancer stem cells

 1 Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, Univ. de Sevilla, Sevilla, C/. Tarfia s/n, 41012, Spain 2 Universidade Federal do Pará, Faculdade de Matemática, Belém, PA 66075-110, Brazil

Received  October 2016 Revised  October 2017 Published  June 2018 Early access  March 2018

In this work we show the existence of coexistence states for a nonlocal elliptic system arising from the growth of cancer stem cells. For this, we use the bifurcation method and the theory of the fixed point index in cones. Moreover, in some cases we study the behaviour of the coexistence region, depending on the parameters of the problem.

Citation: Manuel Delgado, Ítalo Bruno Mendes Duarte, Antonio Suárez Fernández. Nonlocal elliptic system arising from the growth of cancer stem cells. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1767-1795. doi: 10.3934/dcdsb.2018083
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References:
Coexistence region of ($1$) for $\delta\neq 1$
Possible coexistence region of ($1$) for $\delta = 1$. In this case the sum of the index of the coexistence states of ($1$) is 1
Possible coexistence region of ($1$) for $\delta = 1$. In this case the sum of the index of the coexistence states of ($1$) is -1
Possible coexistence region of ($1$) for $\delta = 1$. In this case, there are regions where the sum of the index of the coexistence states of ($1$) is 1 (when $\mathcal{F}_1$ is above $\mathcal{G}$) and others where the sum is -1 (when $\mathcal{G}$ is above $\mathcal{F}_1$)
Coexistence regions of ($1$) for $\delta$ close to 0
Coexistence regions of ($1$) for $\delta$ close to 1

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