Perron Theorem in the Monotone Iteration Method for Traveling Waves in Delayed Reaction-Diffusion Equations

Propagation of Delayed Lattice Differential Equations without Local Quasimonotonicity

This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory of lattice differential equations without time delay. The minimal wave speed of invasion traveling wave solutions is established by presenting the existence and nonexistence of traveling wave solutions.

Traveling Wave Solutions for Delayed Reaction-Diffusion Systems and Applications to Lotka-Volterra Competition-Diffusion Models with Distributed Delays

This paper is concerned with the traveling wave solutions of delayed reaction-diffusion systems. By using Schauder's fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Using the technique of contracting rectangles, the asymptotic behavior of traveling wave solutions for delayed diffusive systems is obtained. To illustrate our main results, the existence, nonexistence and asymptotic behavior of positive traveling wave solutions of diffusive Lotka-Volterra competition systems with distributed delays are established…

Existence of Traveling Waves of Lotka Volterra Type Models with Delayed Diffusion Term and Partial Quasimonotonicity

This paper is concerned with the existence of traveling wave solutions for diffusive two-species Lotka-Volterra systems with delay in both the reaction and diffusion terms without monotonicity. We extend the partial or cross monotone iteration method to systems that satisfy the partial quasi-monotone condition via construction appropriate upper and lower solutions. This is done by using Schauder's fixed point theorem.

Stability of traveling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects

This paper deals with traveling wavefronts for temporally delayed, spatially discrete reaction-diffusion equations. Using a combination of the weighted energy method and the Green function technique, we prove that all noncritical wavefronts are globally exponentially stable, and critical wavefronts are globally algebraically stable when the initial perturbations around the wavefront decay to zero exponentially near minus infinity regardless of the magnitude of time delay.

Traveling Waves in a Three Species Competition-cooperation System

This paper studies the traveling wave solutions to a three species competition cooperation system. The existence of the traveling waves is investigated via monotone iteration method. The upper and lower solutions come from either the waves of KPP equation or those of certain Lotka Volterra system. We also derive the asymptotics and uniqueness of the wave solutions. The results are then applied to a Lotka Volterra system with spatially averaged and temporally delayed competition.

抛物型随机时滞偏微分方程的不变流形

Invariant manifolds for stochastic delayed partial differential equations of parabolic type

本文针对抛物型随机时滞偏微分方程，通过共轭变换、Lyapunov-Perron方法及谱间隙条件分析，证明了其稳定与不稳定不变流形的存在性与光滑性，并将结果应用于随机单物种种群模型。