Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.     

二阶非线性时滞差分方程解的振动性

研究了二阶非线性时滞差分方程△(α_n(△(x_n+p_nx_(n-r)))~γ)+bn(△(x_n+p_nx_(n-T)))~γ+f(n,x_(n-σ))=0给出方程振动的充分条件,推广和改进了中立时滞差分方程的许多结果.     

Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.     

关于Mate-Nevai型非线性积分不等式

主要目的是将Mate-Nevai型积分不等式推广到非线性情形,得到了两个具有广泛意义的Mate-Nevai型非线性积分不等式,利用所得结论讨论某些积分方程解的有界性.     

带有治疗函数及免疫损失率的SIRS流行病模型的动力学分析

本文研究一类带有非线性发病率、新生儿垂直传播、疫苗接种及治疗能力的SIRS传染病模型的动力学行为,该模型充分考虑了医疗资源的局限性,可用医疗资源的供应效率,当感染的数量低于容量时,治疗率与感染的数量成正比,而当感染数量达到容量时,治疗率为常数.在一定条件下,证明了该模型存在后向分支,这意味着边界平衡点与一个正平衡点共存.在这种情况下,控制基本再生数R0小于1不足以控制和根除这种疾病,需要采取额外的措施来确保其解趋近于边界平衡点.当基本再生数R0大于1时,由于治疗、疫苗接种、免疫损失和其他参数的影响,该模型可能存在多个正平衡点.本文分析了该模型平衡点的存在性和稳定性,得到了Hopf分支以及BT分支的存在性,进而发现不稳定极限环及同宿轨道的存在性,并且通过数值模拟来验证所得结果.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

ThemainpurposeofthispaperistoextendandimprovesomeoftheresultsofSighandKusano[4]forequationtothefollowingmoregeneraldifferentialequationoftheformwheren32andL0x(t)=x(t),LKx(t)=1≤k≤n.pi,gandf:[a,∞)→RandH:[a,∞)xRn→Rarecontinuousfunctionswithpi(t)>0,1≤i≤(n-1),pn(t)=1,andg(t)→∞ast→∞.ThedomainD(L.)ofL,,isdefinedtobethesetofallfunctionsx:[Tx,co)-RsuchthatLix(t),05i5nexistandarecontinuouson[Tx,co).Inwhatfollowsbyasolutionof(2)wemeanthatafunctionxED(L.)whichsatisfies(2)forallsufficien…     

Research Announcements Oscillon of Second Order Matrix Differntial Systems

ＲＥＳＥＡＲＣＨＡＮＮＯＵＮＣＥＭＥＮＴＳＯｓｃｉｌｌａｔｉｏｎｏｆＳｅｃｏｎｄＯｒｄｅｒＭａｔｒｉｘＤｉｆｆｅｒｅｎｔｉａｌＳｙｓｔｅｍｓＭｅｎｇＦａｎｗｅｉ（孟凡伟）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ），Ｓｈａｎ...     

二阶线性矩阵微分系统的振动性

本文研究了矩阵微分系统（P（t）Y′）′＋Q（t）Y＝0，t∈［t0，∞）．其中P，Q和Y是n×n实连续矩阵函数，且P（t）和Q（t）是对称的．P（t）是正定矩阵（P（t）＞0，t∈［t0，∞））．利用推广的Riccati变换，得到了系统（1）振动的若干新判据．所得结果改进了Erbe，Kong和Ruan的相应结果．     

大孔树脂对磺酸类化合物吸附行为的研究

用4种大孔树脂ND-022，ND-900，NDA-99和NDA-100作为吸附剂，分别对水溶液中甲基磺酸钠、苯磺酸钠、对甲基苯磺酸钠和2-萘磺酸钠等磺酸盐进行吸附．探讨了溶液的初始pH值对不同类型树脂吸附磺酸类物质的影响，并通过动态吸附实验研究了SO4^2-对树脂吸附磺酸盐的影响．实验结果表明，复合功能树脂NDA-99对磺酸类化合物具有良好的吸附性能，且其选择性优于弱碱树脂ND-900，这为进一步研究大孔树脂对磺酸类物质的吸附机理和实际工业应用提供了一定的理论依据。     

一类新型具有两个独立变量的不连续函数的积分不等式

主要研究了具有两个独立变量的不连续函数(有跳跃间断点)的一类更为广泛的新型积分不等式(Wendroff型),得出了一些新的结论,从而推广了前人的工作.