脉冲喷洒杀虫剂的植物病害模型的周期解

本文研究脉冲喷洒杀虫剂的植物病害模型.考虑在传染率随时间周期变化和森林树木总数保持不变的条件下,讨论具有垂直传播的一类具有单个种群的脉冲喷洒农药的SIRS模型,根据单值算子和Bohl-Brouaser不动点理论证明了无病周期解存在性,并且利用单值矩阵,Floquet理论得到其基本再生数并且给出了其无病周期解局部渐近稳定的条件.     

Weighted pseudo almost periodic solutions of N-th order neutral differential equations with piecewise constant arguments

In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.     

Square-mean almost periodic solutions to some stochastic evolution equations

This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called "Acquistapace–Terreni" conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.     

Similarity degrees for the crossed product of von Neumann algebras

In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.     

Landesman–Lazer Type Conditions and Multiplicity Results for Nonlinear Elliptic Problems with Neumann Boundary Values

We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.     

Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems

In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(a(x, Du)+ F(u)) ■ f in Ω, where f ∈ L1 Ω. A vector field a(·,·) is a Carath′eodory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.     

《微分方程数值解》课程教学改革的探索和实践

结合近几年数学学院信息与计算科学专业微分方程数值解课程的教学实践,本文对该课程的教学内容、教学方法和手段,及以科研促教学等方面进行了探讨.     

连串反应中控制火焰的耦合GKS-CGL方程组解的极限行为

本文考虑连串反应中控制火焰的耦合广义Kuramoto Sivashinsky-Ginzburg Landau(GKS-CGL)方程组的周期初值问题,主要研究其解在系数g→0和δ→0时的极限行为.首先,采用Galerkin方法,通过构造一系列精细的先验估计,得到GKS-CGL方程组周期初值问题整体光滑解的存在唯一性.其次,利用一致有界估计证得GKS-CGL方程组极限解收敛,并给出解的收敛率估计.     

一道错解例题引发的探究性教学

南方出版社出版的高中学业水平考试达标测评丛书《系统集成》（2014年湖南省专用）第64页有这么一道例题： 题目设函数f（x）=a·b,其中向量a=（cos2x＋1,1）,b=（1,3（1/2）sin 2x＋m）.（1）求f（x）的最小正周期;（2）当x∈[0,π6]时,-4〈f（x）〈4恒成立,求实数m的取值范围．     

Morse理论及其在一类N-Laplacian方程中的应用

研究了一类次临界增长的N-Laplacian方程.利用Trudinger-Moser不等式和Morse理论,证明了在不具有山路引理的几何性质、不满足Ambrosetti-Rabinowitz条件及整体符号条件下,该方程非平凡解的存在性.