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arXiv · 2203.14174

Almost-periodic ground state of the non-self-adjoint Jacobi operator and its applications

Xing Liang·Honngze Wang·Qi Zhou
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Abstract

We study the ground states of the one-dimensional non-self-adjoint Jacobi operators in the almost periodic media by using the method of dynamical systems. We show the existence of the ground state. Particularly, in the quasi-periodic media, we show that the lower regularity of coefficients can guarantee the existence of ground states. Besides that, we give two applications: the first application is to show the existence and uniqueness of the positive steady state of the discrete Fisher-KPP type equation; the second application is to investigate the asymptotic behavior of the discrete stationary parabolic equation with large lower order terms.

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Xing Liang, Honngze Wang, Qi Zhou. 2022-03-27. Almost-periodic ground state of the non-self-adjoint Jacobi operator and its applications. https://arxiv.org/abs/2203.14174

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