具有非局部效应的时滞SEIR系统的周期行波解

该文研究了一类具有非局部效应和非线性发生率的时滞SEIR系统的周期行波解.首先,定义基本再生数R₀并构造适当的上下解,将周期行波解的存在性转化为闭凸集上非单调算子的不动点问题,利用Schauder不动点定理结合极限理论建立该系统周期行波解的存在性.其次,利用反证法结合比较原理,建立当基本再生数R₀<1时该系统周期行波解的不存在性.     

时滞周期系统周期解的存在性

文献[1]利用辅助函数及不动点定理讨论了时滞周期系统周期解的存在性,给出了几个充分性判别准则,在这些准则中都要求辅助函数定正、凸且具有无穷小上界,本文试图利用两个辅助函数和不动点定理对系统(1)进行讨论,得到了     

无穷时滞泛函微分方程的正周期解

利用范数形式的锥拉伸和锥压缩不动点定理讨论具有无穷时滞泛函微分方程的周期解问题,获得了正周期解的存在性定理,并给出了定理的若干应用.     

无穷时滞泛函微分方程的正周期解

利用范数形式的锥拉伸和锥压缩不动点定理讨论具有无穷时滞泛函微分方程的周期解问题,获得了正周期解的存在性定理,并给出了定理的若干应用.     

一类积分微分包含的周期解

研究了一类积分微分包含的周期解,利用Kakutani不动点定理和Tichonoff不动点定理给出了凸和非凸两种情形下周期解存在的充分条件.     

一类时滞微分方程正周期解的存在性

应用锥不动点定理研究了一类时滞微分方程周期解的存在性问题,建立了该系统具有至少一个正周期解的充分条件.     

具有部分单调性的时滞扩散方程组行波解的存在性

就一类具有部分单调性的时滞扩散方程组，我们证明了其行波解的存在性．所采用的方法是通过该系统的适当上、下解构造了Banach空间中的闭凸子集，然后应用Schauder不动点定理，证明相关算子在其上存在不动点．作为该结果的一个重要应用，我们考虑一类时滞的捕食与被捕食模型，证明了其行波解的存在性。     

具有状态依赖时滞的脉冲微分的方程周期解的存在性

研究一类具状态依赖时滞的脉冲微分方程的周期解的存在性,利用锥不动点定理获得了关于周期解存在的一些结果.     

一类广义Lasota-Wazewska模型的正概周期解

本文研究了一类广义的Lasota-Wazewska模型的正概周期解,通过转化模型为一个等价的积分方程,并利用非增算子的锥上不动点定理,建立了该模型正概周期解存在性的新结果,对照已有的工作,本文的方法是新颖的.     

一类脉冲泛函微分方程正周期解的存在性

利用锥上的Krasnoselskii不动点定理 ,证明了一类脉冲泛函微分方程正周期解的存在性 .     

Existence of positive periodic solutions of impulsive functional differential equations with two parameters

In this paper, we employ a well-known fixed-point index theorem to study the existence and non-existence of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. Several existence and non-existence results are established.     

Traveling Wave Solutions for Planar Lattice Differential Systems with Applications to Neural Networks

We obtain some existence results for traveling wave fronts and slowly oscillatory spatially periodic traveling waves of planar lattice differential systems with delay. Our approach is via Schauder's fixed-point theorem for the existence of traveling wave fronts and via S¹-degree and equivarant bifurcation theory for the existence of periodic traveling waves. As examples, the obtained abstract results will be applied to a model arising from neural networks and explicit conditions for traveling wave fronts and global continuation of periodic waves will be obtained.     

POSITIVE SOLUTIONS TO m-POINT BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION WITH p-LAPLACIAN

In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel'skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained.     

Existence of traveling wave solutions for influenza model with treatment

To investigate the spreading speed of influenza and the influence of treatment on the spreading speed, a reaction–diffusion influenza model with treatment is established. The existence of traveling wave solutions is shown by introducing an auxiliary system and applying the Schauder fixed point theorem. The non-existence of traveling wave solutions is proved by a two-sided Laplace transform, which needs a new approach for the prior estimate of exponential decay of traveling wave solutions.     

Traveling waves in an SEIR epidemic model with a general nonlinear incidence rate

ABSTRACT

We study the traveling waves of reaction-diffusion equations for a diffusive SEIR model with a general nonlinear incidence. The existence of traveling waves is determined by the basic reproduction number of the corresponding ordinary differential equations and the minimal wave speed. Its proof is showed by introducing an auxiliary system, applying Schauder fixed point theorem and then a limiting argument. The non-existence proof is obtained by two-sided Laplace transform when the speed is less than the critical velocity. Finally, we present some examples to support our theoretical results.     

Local superlinearity for elliptic systems involving parameters

We study the existence, non-existence, and multiplicity of positive solutions for a class of systems of second-order ordinary differential equations using the fixed-point theorem of cone expansion/compression type, the upper-lower solutions method, and degree arguments. We apply our abstract results to study semilinear elliptic systems in bounded annular domains with non-homogeneous boundary conditions. Here the nonlinearities satisfy local superlinear assumptions.     

Non-monotone traveling waves and entire solutions for a delayed nonlocal dispersal equation

This paper is concerned with the traveling waves and entire solutions for a delayed nonlocal dispersal equation with convolution- type crossing-monostable nonlinearity. We first establish the existence of non-monotone traveling waves. By Ikehara’s Tauberian theorem, we further prove the asymptotic behavior of traveling waves, including monotone and non-monotone ones. Then, based on the obtained asymptotic behavior, the uniqueness of the traveling waves is proved. Finally, the entire solutions are considered. By introducing two auxiliary monostable equations and establishing some comparison arguments for the three equations, some new types of entire solutions are constructed via the traveling wavefronts and spatially independent solutions of the auxiliary equations.     

Oscillatory waves in reaction–diffusion equations with nonlocal delay and crossing-monostability

This paper is concerned with the existence of oscillatory waves in reaction–diffusion equations with nonlocal delay and crossing-monostability, which include many population models, and two main results are presented. In the first one, we establish the existence of non-monotone traveling waves from the trivial solution to the positive equilibrium. The approach is based on the construction of two associated auxiliary reaction–diffusion equations with quasi-monotonicity and a profile set in a suitable Banach space by using traveling fronts of the auxiliary equations. In the second one, we obtain the existence of periodic waves around the positive equilibrium by using Hopf bifurcation theorem.     

Periodic positive solutions for adelay nonlinear differential equation with piecewise constant arguments

Using a fixed-point theorem in cone, existence criteria are proved for the periodic positive solutions of a delay differential equation with piecewise constant arguments. Several examples concerning biological models for the survival of red blood cells are given.     

Fixed points and quasi-equilibrium problems

A fixed-point theorem for compact acyclic maps defined on convex subsets of notnecessarily locally convex topological vector spaces is applied to the existence of solutions of quasi-equilibrium problems. Such existence theorems extend known ones which were used for unified approaches to quasi-variational inequalities in [1–5] and others.