Lévy过程驱动的随机泛函积分-微分方程的概周期解（英文）

本文研究一类Levy过程驱动的无穷维随机泛函积分-微分发展方程.在一些合适的条件下,使用算子半群理论和不动点方法,这些方程的概周期温和解的存在唯一性被讨论.进一步,为了说明我们的结果,一个例子被提出.     

一类平面七次多项式系统赤道环的稳定性与极限环分支

本文研究一类平面七次多项式系统赤道环的稳定性和极限环分支，给出了系统的前12个奇点量公式，可积性条件及在赤道附近存在3个极限环的条件，较为精细地指出了极限环的存在位置。     

非自治线性时滞微分方程的扰动全局吸引性及一致稳定性

本文研究非自治线性时滞微分方程的扰动全局吸引性及一致稳定性，主要讨论了线性部分为周期系数与非周期系数的两种情形，获得了关于零解全局吸引及一致稳定的充分条件．推广了文献中线性部分为自治情形的结果。     

GLOBAL ATTRACTIVITY FOR AMULTIPLICATIVE DELAY DIFFERENTIAL POPULATION MODEL

1IntroductionInthispaper-wegiveasufficientconditionwhichguaranteestheg10balattractivityofthepositiveequilibriumofamu1tiplicativede1ayLogisticequation:wasproposedbyHutchinson[1]asamode1fortliegrowthofasing1especies.Equation(1.2)anditsgeneralizati0nhavereceivedandc0ntinuestoreceivegreatattenti0nssee,forexample[1,2,3,8].Inanattempttointroduceseveralenioronmentalnegativefeedbackeffects,manyau-thorshaveinvestigatedthefollowingequation[4,5,7]:However-itisn0tknownwhetherseveraleniv0ronmentalintraspe…     

OSCILLATION CRITERIA FOR SECONDORDER NONLINEAR NEUTRALDIFFERENTIAL EQUATIONS

1IntroductionConsiderthesecondordernonlinearneutraldelaydifferentialequationwheret2to,rando4renonnegativeconstants,a3p,qEC([to,co);R),fEC(R;R).Throughoutthispaper,weassumethatItiswellknownthatthesecondorderneutraldifferentialequationshavemanyapplicationsintheproblemsdealingwithsuchasvibratingmassesattachedtoanelasticbarandsomevariationalproblems(seeHale[1]).ManyauthorshasextensivelyinvestigatedtheoscillationofEq.(E)anditsspecialcases.Forexample,Horng-JaanLiandWei-LingLiuL2'3]andRuan[41…     

脉冲强迫非线性时滞微分方程的渐近性

本文研究一类脉冲强迫非线性时滞微分方程的渐近性,所得结果不仅适用于线性方程和非线性方程,强迫方程和非强迫方程,脉冲方程和非脉冲方程,而且改进了最近文献［８］的主要结果．     

具分布偏差变元非自治数学生态学方程的全局渐近稳定性

本文研究具分布偏差变元非自治微分方程x＇（t）＝－g（t，x（t））－f（t，x（t＋s）du（s））零解的渐近稳定性．方程（1）包含了许多数学生态学方程．文中结论推广和改进了已有文献中相应结果．     

比较原理与Markov调制的随机时滞系统的稳定性

建立了Markov调制的具可变时滞的随机非线性系统的比较原理, 并用比较原理给出了系统依概率稳定、概率渐近稳定、 p阶均值稳定、 p阶均值渐近稳定、 p阶均值指数稳定的判别准则.最后举例说明了文中结果的应用.     

Comparison principle and stability criteria for stochastic differential delay equations with Markovian switching

In the present paper we first obtain the comparison principle for the nonlinear stochastic differential delay equations with Markovian switching. Later, using this comparison principle, we obtain some stability criteria, including stability in probability, asymptotic stability in probability, stability in thepth mean, asymptotic stability in the pth mean and the pth moment exponential stability of such equations. Finally, an example is given to illustrate the effectiveness of our results.     

ASYMPTOTIC BEHMIOR OF SOLUTIONS OF FORCED NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

1Introduction,l,llisl)al'oric(:oil(f(il.[lc(lwil,llt,li',asyTnljtoticbehaviol'ofsollltionsof'II()rllilloa,rI'(f)I.c(}drtolll,ralohffi}r(3rltiil.l(1(]l.lal}io[lsinthe[(,ifillofall(.3r~pi,qj,reC([t.,,co),R),n)cy20,i=l,2,...)rugj=1,2,...SJr).,fEC(R,It)alldxf(x)>0f<)rx/0.Asiscusl,olllary,asolutiolliscalledoscillatoryifithasarbitrarilylarg(3z(3ros;othorwis(3,it,iscalls(ll.lonoscillatory.*'lthiswol.kisstlpl)')rtedbyNSlaof'ChinllandHunanProvince.Manuscriotreceivedit.()(iolll,ly,J.YallII]()[)1…