IMPASSE POINTS AND REDUCTION OF QUASILINEAR DAES WITH INDEX-K

1Introduction(lollsi(l(ir(flllasililloa,l'(hfF(31,')rll,ial()(f[llal.ionfw[1(ireA:UI'-L(It")atldG:U"-It"ar(3ofCZfullctionsoilU".l./"isa,coml)a':t.sllbs')1,of'it".if,isofmor(3intereststoscholars.B(?causco.rill(:I.allk,it,(:al['tl)(1lie(luc(3(l10(lailya,rlOI)li:sviatileiltnl)licitfuTlctiollill'3()r'ltll,wlliclld(?t,(31.llflill'3(1bombssp(i(:ialfcaturos.II'irstly,itImlyhavcrl'l,uni(lll(}solllt,iorll,()IVI'f;r(0)=blotj?(0)=po,it'(x,,p,)=0,if'ilcquil.essolTlecol'Tlf)a,1,il)ilit,y'StJI)l,o…     

OSCILLATORY AND ASYMPTOTIC BEHMIOUR OF A CLASS OF NONLINEAR DIFFERENTIALEQUATIONS OF THIRD ORDER

1IntroductionInthispaperwedealwithoscillatoryandnonoscillatorybehaviourofsolutionsofnonlinearthirdorderdifferentialequationsoftheformwherea,b,cEC([er,co),R),rrER,fEC(R,R)suchthatac2P>0fory/0and7>0isaquotientofoddintegers.From"Theoryofequations"tsee[1],itfollowsthattheequationwithconstantcoefficientsMoreover,allnonoscillatorysolutionsof(1.3)tendtozeroifandonlyifequatioll(l.3)hasanoscillatorysolution.Theseobservationsarefoundtobetruetoalargeextentformoregeneralequationsoftheformwherealb,cE…     

PERIODIC SOLUTION AND ASYMPTOTICITY OF ABEL EQUATION

Inarticles[1]and[2]theexistenceandstabilityofperiodicsolutionofAbelequation:werediscllsscd,wb')lteth'3coefficientsa(t),b(t),c(t)andd(t)areradalcollt,inuouslyp(3riodicfunctions.111thispal)erwenotonlystudythegeneralI\)rnlofeqllation(A),hiltalsodiscllssitssomespecialcases.FOT'example,as(l(l-)=0l,hcAbelequationbecomesfWeshallobtainsomeinterestingresultsfromit,suchdoubleperiodicsolution,etc.Equation(B)alsohassomeapplication,weknowthattheOdum(1971)*ThispaperissponsoredbyNationalScienceFundation…     

LONG TIME ASYMPTOTIC BEHAVIOR OF SOLUTION OF DIFFERENCE SCHEME FOR A SEMILINEAR PARABOLIC EQUATION (Ⅱ)

1.IntroductionLetfi~(0,l),f(x)EH'(fl),"o(x)EH'(fl)nHI(fl),of(u)=u3,weconsiderthefollowinginitial-boundaryvalue'problem:Bytheusualapproach[1--4]wecangettheglobalexistenceofthesolutionof(1.1),furthermore,thesolutionof(1.1)convergestothesolutionofthefollowingstationaryproblem(1.2)ast-co.l)TheProjectissupportedbyChillaPostdoctoralScienceFoundationandtheScienceFoundationofAcademyofEngineeringPhysicsofChinaIn[6]5[7]?theauthorsconsideredtheexplicitschemefor(l.l)asf(x)=0andonlytheestimateinLZf…     

ON THE REGULARITY AND EXISTENCE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS OF SECOND ORDER

Let Ω(?)R~n be a bounded domain with a smooth boundary (?)Ω L a strictly elliptic operator and c(x)≥0 in Ω. In this paper we are concerned with the following Dirichlet problem with the growth condition (P_1): a<2, for n=2. It is proved that if p(x, t) has all derivatives up to order l which are locally Hlder continuous in (?)×R. and if a_(ij)(x) ∈C_(l 1,α)(Ω) and c(x)∈C_(l,α)(Ω), then any weak solution in W_0~(1,2) of (1) lies in C_(l 2,α)(Ω). Moreover, under the growth condition (P_1) and some additional assumptions, the existence of nontrivial solution of (1) is proved. The main difficulity here is that the simple bootstrapping procedure fails to apply directly to the case of the growth condition (P_1).     

THE RATES OF CONVERGENCE OF M-ESTIMATORS FOR PARTLY LINEAR MODELS IN DEPENDENT CASES

51.IntroductionAnembeddingofacoveringmaporaprincipalG-bundleT:E- Xintoavectorbundlep:V→XisamapH:E-VwhichmapsEhomeomorphicallyontoitsimageH(E)inVsuchthatpoH=7.In[6l,HansenprovedthatanyfinitecoveringmapoveraCW-complexcanbeembeddedintothetrivialrealm-planebundleifdimX5m 1.Embeddingfinite..covringmapsintoarbitraryvectorbundleswasconsideredbyDuval1andHuschl3].Suchanembeddingproblemwasalsodiscussedin[4,5,6,7,8,11,12]and[13].Inthisnote,thefirstpoilltistostudyingreaterdepththeembeddingproble…     

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…     

EXISTENCE AND UNIQUENESS OF GLOBAL SOLUTIONS OF ON R~2

1.IntroductionandMainResultThenonlinearSchr6dingerequationshavebeenextensivelystudiedin[3,5,6,8,9],whereequationsareofthefollowingtype:In[l],anothertypeofequationshasbeenstudiedSincetheequalityofenergydoesnothold,theGalerkinmethodisused.Inthispaper)wewillstudythepropertyofequationsofthe'secondtype,wherewemakethechoiceoffi=R:.BecauseoftheunboundednessofR',wecannotusetheGalerkinmethod,andweuseothermethodtoobtaintheaDDroximatesolutions.Inthispaper,firstlyweconsidertheglobalweaksolutionsofthe…     

HOMOGENIZATION OF SOME LINEAR AND SEMILINEAR SCHRDINGER EQUATIONS WITHREAL POTENTIAL

1 IntroductionIn this paPer, we collsider the initial and boundaxy value probIem of linear and sentilillearScl1r5dinger equation as fOllows:l ie(x):5:i".,'<">"'>.'<",,'>,"=' 1:!\:?0t:)t>, (l1)wllere E > 0, fl C RN is a bounded open dolllain and T is an ar…     

Pseudo-almost periodic solutions of neutral integral and differential equations with applications

The existence and uniqueness of pseudo-almost periodic solutions to general neutral integral equations with deviations are obtained. For this, pseudo-almost periodic functions in two variables are considered. The results extend the corresponding ones to the convolution type integral equations. They are used to study pseudo-almost periodic solutions of general neutral differential equations and to the so-called scalar neutral logistic equation version.     

NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF NEUTRAL LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS：A METHOD BY FOURIER SERIESES

ＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＳＦＯＲＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＮＥＵＴＲＡＬＬＩＮＥＡＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴ...     

Some results on second-order neutral functional differential equations with infinite distributed delay

In this paper, we consider two types of second-order neutral functional differential equations with infinite distributed delay. By choosing available operators and applying Krasnoselskii’s fixed-point theorem, we obtain sufficient conditions for the existence of periodic solutions to such equations.     

脉冲中立型时滞微分方程的正解的存在性

本文证明了线性脉冲中立型微分方程 [y(t)+p(t)y(t-τ)-r(t)y(t-ρ)]′+q(t)y(t-σ)=0,t≥0,t≠t_k, y(t_k~+)-y(t_k)=b_ky(t_k),k=1,2,…正解的存在性等价于一类非脉冲中立型方程正解的存在性,应用这一结果,建立了此类线性脉冲中立型微分方程正解存在性的若干充分条件。     

Stability of a critical nonlinear neutral delay differential equation

This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the fact that the spectrum of the linear operator is asymptotically closed to the imaginary axis. An analysis based on the energy method provides new results about the asymptotic stability of constant and periodic solutions. A complete analysis of the stability diagram is given in the linear homogeneous case. Under periodic forcing, existence of periodic solutions is discussed, involving a Diophantine condition on the period of the source.     

中立型泛函微分方程的周期解

对于中立型泛函微分方程,证明了解的毕竟有界性蕴含周期解的存在性,把常微分方程中著名的Yoshizawa周期解存在定理推广到中立型泛函微分方程,然后利用所得结果给出一类产生于电力系统的中立型时滞泛函微分方程周期解存在惟一与吸引的条件。     

The differential equations on time scales through impulsive differential equations

In this paper we investigate differential equations on certain time scales with transition conditions (DETC) on the basis of reduction to the impulsive differential equations (IDE). DETC are in some sense more general than dynamic equations on time scales [M. Bohner, A. Peterson, Dynamic equations on time scales, in: An Introduction With Applications, Birkhäuser Boston, Inc., Boston, MA, 2001, p. x+358; V. Laksmikantham, S. Sivasundaram, B. Kaymakcalan, Dynamical Systems on Measure Chains, in: Math. and its Appl., vol. 370, Kluwer Academic, Dordrecht, 1996]. The basic properties of linear systems, the existence and stability of periodic solutions, and almost periodic solutions are considered. Appropriate examples are given to illustrate the theory.     

Periodic solutions of abstract neutral functional differential equations with infinite delay

We establish the existence of mild solutions and periodic mild solutions for a class of abstract first-order non-autonomous neutral functional differential equations with infinite delay in a Banach space. This research was supported by FONDECYT-CONICYT, Grant 1050314.     

Asymptotic equivalence of differential equations and asymptotically almost periodic solutions

In this paper we use Rab’s lemma [M. Ráb, Über lineare perturbationen eines systems von linearen differentialgleichungen, Czechoslovak Math. J. 83 (1958) 222–229; M. Ráb, Note sur les formules asymptotiques pour les solutions d’un systéme d’équations différentielles linéaires, Czechoslovak Math. J. 91 (1966) 127–129] to obtain new sufficient conditions for the asymptotic equivalence of linear and quasilinear systems of ordinary differential equations. Yakubovich’s result [V.V. Nemytskii, V.V. Stepanov, Qualitative Theory of Differential Equations, Princeton University Press, Princeton, New Jersey, 1966; V.A. Yakubovich, On the asymptotic behavior of systems of differential equations, Mat. Sb. 28 (1951) 217–240] on the asymptotic equivalence of a linear and a quasilinear system is developed. On the basis of the equivalence, the existence of asymptotically almost periodic solutions of the systems is investigated. The definitions of biasymptotic equivalence for the equations and biasymptotically almost periodic solutions are introduced. Theorems on the sufficient conditions for the systems to be biasymptotically equivalent and for the existence of biasymptotically almost periodic solutions are obtained. Appropriate examples are constructed.     

Periodic solutions of neutral fractional differential equations

We characterize the existence of periodic solutions for some abstract neutral functional fractional differential equations with finite delay when the underlying space is a UMD space.