Stability of Linear Integrodifferential Systems with Time-varied Confficients with Large Scale

51.IntroductionConsideralinearintegrodifferentialsystemswithtime-variedconfficientswherex6R",A(t)isanXnrealmatrixfunctioncontinuousforoO.ManyscholarshavecontributedtheirpaPers[1-4]todiscussstabilityofzerosolutionofsystem(1.l).Inthispaper,weassumethatsystem(1.1)canbedecomPOsedintotheform=n,A,j(t)isaniXnjrealmatrixfunctioncontinuousforo相似文献   

An Oscillation Criterion for Second Order Superlinear Differential Equations

61.IntroductionConsiderthesecondordersuperlinearequationx'(t) p(t)X'(t) q(t)1x(t)l"sgnx(t)=o,t>to,(1)wherea>l,pandq:[t,'co)-R=(-co,oo)arecontinuous.Weconsideronlysuchsolutionsxofequation(l)whichexistonsomeinterval[t.,oo),t.>t,>o.Asolutionofequation(l)issaidtobeoscillatoryifithasarbitrarilylargezerosandotherwise,itissaidtobenonoscillatory.Equation(l)iscalledoscillatoryifallofitssolutionsareoscilllatory.Forthespecialcasewherep(t)=Oli.e.,forthedifferentialequationx'(t) q(t)lx(t)l"sgnx(t)=o,a>1-…     

ON DETERMINATION OF THE IMPULSIVESOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS

1IntroductionInthispaper,wediscussthecompletesolutionoftheLinearNon-HomogeneousMatrixDifferentialEquations(LNHMDEs)describedbyA(p)PNH(t)=B(p)U(t),t2o,(1)wherepgd/dtthedifferentialoperator,A(p)=A,,Pq' A,,-1Pq1-' ' A1p AoERfa],",,rankR(.)A(p)=rlAieR",,i=O,1,2,',qi,qi>1,B(p)=Blpl BI-,P,-' -.' B1p BOeR[P],'",BjER'",j=o,1,2,...,l,l2o,PNH(t):[o, oc)-R'isthepseudostateoftheLNHMDE,u(f):[o, oo)-R"isanitimespiecewisecontinuouslydifferentiablefunctioncalledtheinputoftheLNHMDE…     

二阶非线性微分议程解的平方可积性与有界性(英文)

1 IntroductionIn this paPer, we consider the second order nonlinear differential equationwhere r(t) > 0 fOr t E [a, oo) and r(t) is absolutely continuous on [a, oc), p, q1and q2 are real functions defined on [a, oo) and f is a real function defined on[a, oo) x (--oc, oo) which satisfieswhere 0 S cr S 1, g(t) 2 0 and h(t) 2 0 for t E [a, oo).The behaviors of quadratic integrability and boundedness fOr some moreparticular forms of equation (l) such as have been studied (see [1--4]). And many …     

A NOTE ON GLOBAL ATTRACTIVITY OF THE MODEL FOR THE SURVIVAL OF THE RED BLOOD CEELS WITH SEVERAL DELAYS

1 IntroductionConsider the red blood ceels growth model with several delayswhere r(t) E C([0, oo), (0, oo)), Pil ri) n e (0, oo), and r1 2 r2 2'' 2 rm.Eq.(l) was used first by Wazewska-Czyzewska and Lasota [l] as a model forthe survival of the red blood ceels in an animal, see also Arino and Kimmel[2]. There are a lot of activities concerning the asymptotic behavior of (1),see for examp1e [3] and the references cited therein. The following results wasobtained in [l, 3, 4].N'(t) = --pN(t)…     

Oscillation of Neutral Equations withVariable Coefficients

51iIntroductionConsidertheneutralequationwithvariablecoefficientsInrecentyears,thedscillatotytheoryforneutralequathaiswelldeveloped.Inparticular,manydifferentsuffitientconditionsfortheoscillationofallsolutionsofEq.(l)areobtainedin[l-7j.Allthepapersmentionedexcept[6],however,alwaysassumeP(t)isinoneofthefOllowingranges:OSP(t)SlorP(t)2l.Ouraiminthispapertoeatablishnewsufficientcon-ditionsfortheoscillationofallsolutiOnsofEq.(l)underlessrestrictivehypothesesonP(t).Letm=max{Y,d}.Byasolutionof…     

ASYMPTOTICS AND OSCILLATION FOR FIRST ORDER MIXED NEUTRAL DIFFERENTIAL EQUATIONS

1IntroductionConsidertheneutraldifferentialequationswherepiERfori=l,2,...,m;o相似文献   

On the Favard Class of Cosine Operator Function

61.IntroductionLetXbeaBanachspace,B(X)thealgebraofallboundedlinearoPeratoronXandC(t),t6R,thestronglycontinuouscosineoperatorfunctionsonXwithinfinitesimalgeneratorA,TheFavard(orSaturation)classorgeneralizedFav(A)ofcosineoperatorfuctionC(t)withgeneratorAisdefinedbyFav(A)={x:supl,1<,Il2t~'(C(t)-I)xllX oo}.Theestimater'P,llC(t)x-xIl=IlAJoJoC(p)xdedsIl相似文献   

具有变滞量的一阶中立型泛函微分方程的振动性

本文研究具有变滞量的一阶刀夕刀E共[二(,)一。(,)二(,一,)〕+,(,)二〔,一:(,)〕=。,,),。Q了(1)的振动性.文中始终假设::,c,P:[t0,sup:(,)些。<,co,lim[t一r(t)]=+oo,瞪r氏叮睁甘阵卜少E.A.Grove,M.R.S.Kulenovi亡和G.+co),R+连续,r>0,0(c(t)(1(t》t。);存在常数K>o,使得。(K《p(t)(t)t。).Ladas[i]研究了方程(1)中了(t)三eonst.>0的情形,而本文考虑变滞量的情形,给出了方程(1)当。0且y‘(t)(0. …     

ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

1IntroductionInthispaper,weintendtostudytheexistenceoftheglobalattractorforthefollowinginitialvalueproblemofGinzburgLandauequationcoupledwithBBMequationinanunboundeddomainR=(-oo,oo)wheree(x,f)isacomplexfunction,n(x,t)isarealscalarfunction,pty,6,T,cr1,a2,P1,P2arerealcoustants,andg1(x),g2(x)aregivenrealfunctions.ThisproblemdescribesthenonlinearinteractionsbetweentheLangnluirwaveandtheionacousticwaveinplasmaphysics,E(z,t)denoteselectricfield,n(x,t)betheperturbationofdensity(see[2,12,6l).In[7]…     

On the determination of the number of periodic (or closed) solutions of a scalar differential equation with convexity

It is well known that a scalar differential equation , where f(t,x) is continuous, T-periodic in t and weakly convex or concave in x has no, one or two T-periodic solutions or a connected band of T-periodic solutions. The last possibility can be excluded if f(t,x) is strictly convex or concave for some t in the period interval. In this paper we investigate how the actual number of T-periodic solutions for a given equation of this type in principle can be determined, if f(t,x) is also assumed to have a continuous derivative . It turns out that there are three cases. In each of these cases we indicate the monotonicity properties and the domain of values for the function P(ξ)=S(ξ)−ξ, where S(ξ) is the Poincaré successor function. From these informations the actual number of periodic solutions can be determined, since a zero of P(ξ) represents a periodic solution.     

Solutions of the generalized Lennard-Jones system

In this paper, we study solution structures of the following generalized Lennard-Jones system in R~n,x=(-α/|x|~(α+2)+β/|x|~(β+2))x,with 0 α β. Considering periodic solutions with zero angular momentum, we prove that the corresponding problem degenerates to 1-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions.     

On the existence of bounded noncontinuable solutions

This paper presents necessary and sufficient conditions for an n ‐th order differential equation to have a non‐continuable solution with finite limits of its derivatives up to the order l at the right‐hand end point of the interval of its definition, l ≤ n – 2 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Proof for the Equivalence of Weak and Viscosity Solutions for the p-Laplace Equation

In this paper, we give a new proof for the fact that the distributional weak solutions and the viscosity solutions of the p-Laplace equation ?div(|Du| ^p?2 Du) = 0 coincide. Our proof is more direct and transparent than the original proof of Juutinen et al. [8 Juutinen , P. , Lindqvist , P. , Manfredi , J.J. ( 2001 ). On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation . SIAM J. Math. Anal. 33 : 699 – 717 .[Crossref], [Web of Science ®] , [Google Scholar]], which relied on the full uniqueness machinery of the theory of viscosity solutions. We establish a similar result also for the solutions of the non-homogeneous version of the p-Laplace equation.     

一个包含Euler函数的方程

对任意自然数n≥1,著名的Euler函数ψ(n)定义为不大于n且与n互素的正整数的个数.本文的主要目的是研究方程ψ(ψ(ψ(n)))=2ω(n)的可解性,其中ω(n)表示n的所有不同素因子的个数,并给出了该方程的所有正整数解.     

Asymptotic behaviour of the Kazdan-Warner solution in the annulus

In this paper, we study the asymptotic behaviour as p→∞ of the radial solution of the problem

     

On the behavior of the oscillatory solutions of first or second order delay differential equations

Some new results are given concerning the behavior of the oscillatory solutions of first or second order delay differential equations. These results establish that all oscillatory solutions x of a first or second order delay differential equation satisfy x(t)=O(v(t)) as t→∞, where v is a nonoscillatory solution of a corresponding first or second order linear delay differential equation. Some applications of the results obtained are also presented.     

Darboux transformation and explicit solutions for the (2+1)-dimensional nonlocal nonlinear Schrödinger–Maxwell–Bloch system

The $(2+1)$-dimensional nonlocal nonlinear Schrödinger–Maxwell–Bloch system with $PT$-symmetric potentials will be investigated in this paper. The $(2+1)$-dimensional Darboux transformation will be constructed, some explicit solutions including periodic waves solutions, soliton solutions and complexiton solutions will be obtained under different backgrounds, and the interaction behaviors of those solutions will be discussed through some figures.     

两个数论函数及其方程

对于任意给定的自然数n,著名的Eu ler函数φ(n)定义为不大于n且与n互素的正整数的个数.ω(n)表示n的所有不同素因子的个数.本文研究了方程φ(n)=2ω(n)的可解性,并给出了该方程的所有正整数解.