English

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

Dynamical Systems 2022-03-29 v1 Analysis of PDEs Functional Analysis Spectral Theory

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.

Keywords

Cite

@article{arxiv.2203.14174,
  title  = {Almost-periodic ground state of the non-self-adjoint Jacobi operator and its applications},
  author = {Xing Liang and Honngze Wang and Qi Zhou},
  journal= {arXiv preprint arXiv:2203.14174},
  year   = {2022}
}