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Volume 8, Number 5, 2018, Pages 1342-1368                                                                DOI:10.11948/2018.1342
Monotone methods and stability results for nonlocal reaction-diffusion equations with time delay
Yueding Yuan and Zhiming Guo
Keywords:Monotone method, nonlocal reaction term, delay, existence and uniqueness, stability.
      In this paper, we study the applications of the monotone iteration method for investigating the existence and stability of solutions to nonlocal reaction-diffusion equations with time delay. We emphasize the importance of the idea of monotone iteration schemes for investigating the stability of solutions to such equations. We show that every steady state of such equations obtained by using the monotone iteration method is priori stable and all stable steady states can be obtained by using such method. Finally, we apply our main results to three population models.
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