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It is well known that, in the study of the dynamical properties of nonlinear evolution system with nonlocal dispersals, the principal eigenvalue of linearized system play an important role. However, due to lack of compactness, in order to…
It is well known that, in the study of the dynamical properties of nonlinear reaction-diffusion systems, the sign of the principal eigenvalue of the linearized system plays an important role. However, for the nonlocal dispersal systems, due…
The current paper {establishes} criteria for the existence of principal eigenvalues of time periodic cooperative linear nonlocal dispersal systems with Direchlet type, Neumann type or periodic type boundary conditions. It is shown that such…
This paper investigates the principal spectral theory and the asymptotic behavior of the principal spectrum point for a class of time-periodic cooperative systems with nonlocal dispersal operators, incorporating both coupled and uncoupled…
This paper is to investigate the dependence of the principal spectrum points of nonlocal dispersal operators on underlying parameters and to consider its applications. In particular, we study the effects of the spatial inhomogeneity, the…
An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…
In this communication, we prove some important limits of the principal eigenvalue for nonlocal operator of Neumann type with respect to the parameters, which are significant in the understanding of dynamics of biological populations. We…
This paper is mainly concerned with the generalised principal eigenvalue for time-periodic nonlocal dispersal operators. We first establish the equivalence between two different characterisations of the generalised principal eigenvalue. We…
The basic reproduction ratio is a crucial threshold parameter in infectious disease models. In nonlocal dispersal systems, its variational characterization is challenging due to the possible absence of a principal eigenvalue caused by…
The purpose of this paper is to investigate the principal spectral theory and asymptotic behavior of the spectral bound for cooperative nonlocal dispersal systems, specifically focusing on the case where partial diffusion coefficients are…
We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as…
We investigate the effects of advection on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions. Various asymptotic behaviors of the principal eigenvalues, when advection coefficient…
The paper is concerned with the principal eigenvalue of some linear elliptic operators with drift in two dimensional space. We provide a refined description of the asymptotic behavior for the principal eigenvalue as the drift rate…
For fixed $c\in\mathbb R$, $l>0$ and a general non-symmetric kernel function $J(x)$ satisfying a standard assumption, we consider the nonlocal diffusion operator \begin{align*} \bf{L}^{J,…
This work examines the limits of the principal spectrum point, $\lambda_p$, of a nonlocal dispersal cooperative system with respect to the dispersal rates. In particular, we provide precise information on the sign of $\lambda_p$ as one of…
We study the generalized eigenvalue problem in $\mathbb{R}^N$ for a general convex nonlinear elliptic operator which is locally elliptic and positively $1$-homogeneous. Generalizing article of Berestycki and Rossi in [Comm. Pure Appl. Math.…
This paper develops the notion and properties of the generalized principal eigenvalue for an elliptic system coupling an equation in a plane with one on a line in this plane, together with boundary conditions that express exchanges taking…
This paper is devoted to the study of the asymptotic behavior of the principal eigenvalue and basic reproduction ratio associated with periodic population models in a patchy environment for small and large dispersal rates. We first deal…
This paper is concerned with asymptotic persistence, extinction and spreading properties for non-cooperative Fisher-KPP systems with space-time periodic coefficients. Results are formulated in terms of a family of generalized principal…
We study a nonlocal SIS epidemic model with free boundaries, advection, and spatial heterogeneity, where the dispersal kernels are not assumed to be symmetric. The model describes the evolution of susceptible and infected populations in a…