Entire solutions of non-quasi-monotone delayed reaction—diffusion equations with applications
Entire solutions of non-quasi-monotone delayed reaction—diffusion equations with applications
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DOI：
10.1017/s0308210512001412
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发表时间：
2014-10
期刊：
影响因子：
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通讯作者：
Shiliang Wu;Cheng-Hsiung Hsu
中科院分区：
文献类型：
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作者：
Shiliang Wu;Cheng-Hsiung Hsu
本文主要研究非拟单调时滞非局部反应扩散方程的整体解。众所周知，比较原理不适用于这类方程。为了克服这个困难，我们引入了两个辅助的拟单调方程，并建立了三个系统的比较参数。一些新类型的整体解决方案，然后构造使用的比较参数，行波波前和空间独立的解决方案的辅助方程。我们还将我们的论点扩展到具有非单调输出函数的延迟细胞神经网络和具有非单调出生函数的延迟非局部格微分方程。
We are interested in finding the entire solutions of non-quasi-monotone delayed non-local reaction–diffusion equations. It is well known that the comparison principle is not applicable for such equations. To overcome this difficulty, we introduce two auxiliary quasi-monotone equations and establish some comparison arguments for the three systems. Some new types of entire solutions are then constructed using the comparison argument, the travelling wavefronts and a spatially independent solution of the auxiliary equations. We also extend our arguments to a delayed cellular neural network with non-monotonic output functions and a delayed non-local lattice differential equation with non-monotonic birth functions.