ON THE NONEXISTENCE OF PERIODIC SOLUTIONS FOR LIENARD-TYPE EQUATIONS

1.IntroductionConsiderthefollowinggeneralizedLi6nardtypeequationwhereshallowing[1],thisequationwillbecalledasaLi6nard-typeequationofordern.Whenn=1,theequation(1.1)canbewrittenasthefollowingformClearly)whenfi(x)=j(x),f200=0,theequation(1.3)isreducedtothewellknownLi6nardequationx j(x)x g(x)=0.(1.4)Recently,theequation(1.3)hasalreadybeenstudiedwithparticularemphasisontheex-istenceanduniquenessofperiodicsolutionsbyseveralauthors.Forexample,needmanandKuangll],GuidorizzilZ],ZhouJinI3],andJiangJ…     

ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS

In this paper,we use the contraction principle and the Leray-Schauder principleto deal with the existence of periodic solutions of the Volterra integral differential equation.Some new existence criteria and unique existence criteria are obtained.     

GLOBAL CLASSICAL SOLUTIONS AND EXPLICITEXACT SOLUTIONS TO A KIND OF QUASILINEARPARTIAL DIFFERENTIAL EQUATIONS

1.IntroductionandMainResultTherearemanyexamplesconcerningtheformationofsingularitiesinthesoluti0nsofnon-linearpartialdifferefitialequations.Thus,althoughasolutionmaybesmoothinitially,itmaybecomesingularatsomelatertime(see[1-6]).However,T.Nishidahaspr0vedthatiftheCln0rmoftheinitialdataissufficientlysmall,thentheCauchyproblemadmitsauniqueglobalsmooths0lutionont2Otoareduciblequasilinearhyperbolicsystemwithfirst(lower)orderdissipativeterm(see[7]).Thereafter,manyauthorshavegeneralizedNishida'sr…     

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

ASYMPTOTIC STABILITY OF SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR SCALAR VISCOUS CONSERVATION LAWS CORRESPONDING TO RAREFACTION WAVES

1.IntroductionWeconsidertheinitial-boundaryvalueproblem(IBVP)forscalarviscousconservationlaw(ut f(u).=uxx,xE(0, co)=R ,t>0,o,(n \--9,ifI~9,f~M(IBVP){u(0't)=u~(t)-1~i---t:7),[u(x,0)=u000={=:0)f:LO .,wheref"(u)>0foralluunderconsideration,andu--u (1.1),andu~(t)~u~EL'(R ),U'(t)EL'(R ).(1.2)Undercondition(1.l)or(l.l)',thecorrespondingRiemannproblem{;;ot:<:>;i,>=x{,:3'f:,:(13)yieldstherarefaCtionwavesolution(u~)x5f'(u~)t,r"(X,t)=17j,)~1(…     

ON THE EXISTENCE OF MEROMORPHIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＭＥＲＯＭＯＲＰＨＩＣＳＯＬＵＴＩＯＮＳＯＦＡＬＧＥＢＲＡＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＹＵＡＮＷｅｎｊｕｎ（ＤｅｐａｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＮｏｏｒｍａｌＵｎｉｖｅｒｓ...     

均衡函数及其在变权综合中的应用

进一步研究了均衡函数，改进了［４］中公理化体系，获得了两大数均衡函数及相应的变权模式并分析了这些模式之间的关系。     

EXISTENCE OF NONTRIVIAL SOLUTIONS FOR CRITICAL SEMILINEAR BIHARMONIC EQUATIONS

ＥＸＩＳＴＥＮＣＥＯＦＮＯＮＴＲＩＶＩＡＬＳＯＬＵＴＩＯＮＳＦＯＲＣＲＩＴＩＣＡＬＳＥＭＩＬＩＮＥＡＲＢＩＨＡＲＭＯＮＩＣＥＱＵＡＴＩＯＮＳ￥ＧＵＹｏｎｇｇｅｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅ...     

SOME INITIAL-OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS WITH UNBOUNDED COEFFICIENTS

1 IntroductionThis paper is concerned with the a priori estimates and the ekistence of solutions of theinitiaLoblique derivative boundary value problem for quasilinear non-divergence parabolic equa-tions as follows:where O is a bounded domain in R"(N > 2) with smooth boundary 0a e C' ', QT =[o,T) x a be the parabolic domain in H" ,, ST = [o,T) x aa is the lateral boundary, andarQT is the parabolic boundary of QT' The repeated indices means summatiOns from 1 to N.In [11, the first bounda…     

Forced Oscillations of a Class of Nonlinear Dispersive Wave Equations and their Stability

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Korteweg-de Vries （KdV） equation and the damped Benjamin-Bona-Mahony （BBM） equation. In this paper we intend to show the same results hold for the pure KdV equation （without the damping terms） posed on a finite domain. Consideration is given to the initial-boundary-value problem {ut＋ux＋uux＋uxxx=0, u（x,0）=φ（x）, 0〈x〈1, t〉0,u（0,t）=h（t）, u（1,t） = 0, ux（1,t） = 0, t〉0.It is shown that if the boundary forcing h is periodic with small ampitude, then the small amplitude solution u of （＊） becomes eventually time-periodic. Viewing （＊） （without the initial condition） as an infinite-dimensional dynamical system in the Hilbert space L^2（0, 1）, we also demonstrate that for a given periodic boundary forcing with small amplitude, the system （＊） admits a （locally） unique limit cycle, or forced oscillation, which is locally exponentially stable. A list of open problems are included for the interested readers to conduct further investigations.     

BOUNDARY SOLUTIONS OF OPERATOR EQUATIONS IN PARIAL ORDERING SETS WITH APPLICATIONS TO SYSTEMS OF FUNCTIONAL

1.IntroductionThepaPers[l-5]studythecoupledfixedp0intsofmixedmonotoneoperatorsinBanachspaces;theyshowusgeneralizationsofthefixedpoillttheoremsonincreasingoperatorsanddecreasingoperators.Applicationsoftheseresultsmaybefoundinmanyfieldsofmathematicssuchasnonlineaxdifferentialequations,illtegralequationsanddynamicprogrammingtheories.Inthispaper,westudytheekistenceofsolutionsandboundarysolutionstoasystem0foperatorequationsinpartialorderingsets.Wegeneralizeandimproveonsomeresultsaboutthecoupledfix…     

On the Meromorphic Solutions of Linear Differential Equations

In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）, where Pj（z） （j = 0, 1,..., k - 1） are nonconstant polynomials such that deg Pj = n （j = 0, 1,..., k - 1） and Aj（z）（≠ 0） （j = 0, 1,..., k - 1） are meromorphic functions with order p（Aj） 〈 n （j = 0, 1,..., k - 1）.     

FINITE DIMENSIONAL BEHAVIOR FOR THE DISSIPATIVE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATIONS

This paper deals with the asymptotic behaviour of solutions for the generalized symmetric regularized long wave equations with dissipation term. We first show the existence of global weak attractors for the periodic initial value problem of this equations in H2 x H1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the global weak attractor is actually the global strong attractor for S(t) in H2(2) x H1(M).The finite dimensionality of the global attractor is also established.     

STABILITY OF STEADY－STATE SOLUTIONS OF THE COMPETITION MODEL IN THE CHEMOSTAT

ＳＴＡＢＩＬＩＴＹＯＦＳＴＥＡＤＹ－ＳＴＡＴＥＳＯＬＵＴＩＯＮＳＯＦＴＨＥＣＯＭＰＥＴＩＴＩＯＮＭＯＤＥＬＩＮＴＨＥＣＨＥＭＯＳＴＡＴ￥ＷＵＪｉａｎｈｕａ（Ｘｉ＇ａｎＩｎｓｔｉｔｕｔｅｏｆＨｉｇｈｗａｙ，Ｘｉ，ａｎ７１００６４，Ｃｈｉｎａ）ＬＩＹａｎ...     

THE GENERALIZED SOLUTIONS OF PBVP FOR INTEGRO-DIFFERENTIAL EQUATIONS

ＴＨＥＧＥＮＥＲＡＬＩＺＥＤＳＯＬＵＴＩＯＮＳＯＦＰＢＶＰＦＯＲＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＺＨＵＡＮＧＷａｎ；ＣＨＥＮＹｕｂｏ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＮｏｒｍａｌＵｎｉｖｅｒｓ...     

POSITIVE SOLUTIONS OF SINGULAR SUBLINEAR SECOND ORDER BOUNDARY VALUE PROBLEMS

1.IntroductionBoundaryvaluepr0blemsconcerningthegeneralizedEmden-F0wlerequationsx" p(t)x'=O,(1)wherep(t)eC(O,1),p(t)20f0rtE(O,1),AER,havebeenstudiedbymanyauthors(see[1-51andthereferencestherein).InthispaperwetreattheDirichletproblem(1)withax(0)-bx'(0)=O,c…     

EXISTENCE OF MULTIPLE SOLUTIONS AND BIFURCATIONFOR CRITICAL SEMILINEAR BIHARMONIC EQUATIONS

ＥＸＩＳＴＥＮＣＥＯＦＭＵＬＴＩＰＬＥＳＯＬＵＴＩＯＮＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＦＯＲＣＲＩＴＩＣＡＬＳＥＭＩＬＩＮＥＡＲＢＩＨＡＲＭＯＮＩＣＥＱＵＡＴＩＯＮＳＥＸＩＳＴＥＮＣＥＯＦＭＵＬＴＩＰＬＥＳＯＬＵＴＩＯＮＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＦ...     

SOLITON AND ELLIPTICAL PERIODIC SOLUTIONS TO THE MODIFIED NONLINEAR SCHRODINGER EQUATION

1.IntroductionAsiswellknown,theNLSE.02 ac Iql:q=0(1)'N Zap Iql:q=0(1)describesthepropagationofpicosecondOPticalpulseinamonomodeOPticalfiber,whereq(',T)istocomplexpulse,'represelltsthedistancealongthedirectionofpropagation,Trepresentsthetimeinthegroupvelocityframeandrs=11.TheNLSEhasbrightsolitonsolutionwhend==1,anddarksolitonsolutionwhena=11.Inthisnotewehaveobtainedthedarksolitonsolutionwhena~1.However,recentworkshaveshownthattheNLSEisnotsufficieDttodescribethepropagationoffemtosecond…     

AN EXISTENCE THEOREM FOR RADIAL POSITIVE SOLUTIONS OF NONLINEAR DEGENERATE ELLIPTIC EQUATIONS

ＡＮＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＦＯＲＲＡＤＩＡＬＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＤＥＧＥＮＥＲＡＴＥＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＬＩＵＨａｉｌｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｎａｎＮｏ...     

NONTRIVIAL PERIODIC SOLUTIONS OF A SEMILINEAR WAVE EQUATION WITHOUT ASSUMPTION OF MONOTONICITY

In references,some authors have succeeded in obtaining existence re-sults of the superlinear wave equation without the assumption of monotonicity forthe nonlinear term.In this paper,we present existence results for this problem byusing local linking idea and improve some previous results.