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Patterns in a nonlocal time-delayed reaction–diffusion equation

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Abstract

In this paper, the existence, stability, and multiplicity of nontrivial (spatially homogeneous or nonhomogeneous) steady-state solution and periodic solutions for a reaction–diffusion model with nonlocal delay effect and Dirichlet/Neumann boundary condition are investigated by using Lyapunov–Schmidt reduction. Moreover, we illustrate our general results by applications to population models with one-dimensional spatial domain.

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Correspondence to Shangjiang Guo.

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This work was partially supported by the National Natural Science Foundation of P.R. China (Grant No. 11671123).

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Guo, S. Patterns in a nonlocal time-delayed reaction–diffusion equation. Z. Angew. Math. Phys. 69, 10 (2018). https://doi.org/10.1007/s00033-017-0904-7

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  • DOI: https://doi.org/10.1007/s00033-017-0904-7

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