PERIODIC SOLUTIONS OF THE JOSEPHSON EQUATION

In this paper,the Josephson equation and its autonomous case are considered.It isshown that for |α|<1 and β>γ>1 or β<γ<-1,there is no periodic solution of the autonomousJosephson equation,For the nonautonomous case,some suffcient conditions for the existence ofperiodic solutions are given.     

EXISTENCE AND NONEXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS

In this paper an existence theorem of positive radial solutions to a class of semilinear elliptic systems is proved by the Leray-Schauder degree theorem. Also, a nonexistence theorem is obtained. As an application of the main theorem, an example is given.     

A REMARK ON PERIODIC SOLUTIONS OF SINGULAR HAMILTONIAN SYSTEMS WITH SUBLINEAR TERMS

In this paper,we prove the existence of multiple periodic solutionsfor a class of singular Hamiltonian systems with sublinear terms via variationalmethods.     

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.     

BLOW-UP OF SOLUTIONS OF THE IGNITION MODEL

By use of maximum principle and auxiliary function method, the paper dis-cusses the blow-up sets of the solutions of the ignition model in two cases. It is obtained that the solutions blow up in single point in nonsymmetric case and that the solutions blow up totally or at a couple of points in symmetric case.     

THE STABILITY OF NON-AUTONOMOUS DELAY SYSTEMS

The objective of the paper is to derive new simple criteria for the stability of alinear non-autonomous delay system by using a difference-differential inequality.     

THE POLE ASSIGNMENT OF LINEAR SYSTEMS

In this paper the pole assignment problem of a time invariant linear control system issolved by using the Wu Elimination Method.In general,the questions are classified into(i)the poleassignment by using state feedback,(ii)the pole assignment by using output feedback,(iii)the poleassignment via dynamic compensator.The key point of all these problems is to solve a certaincorresponding system of polynomial equations.Based on algebraic geometry,the Wu methodprovides a mechanical algorithm for solving the system of polynomial equations.Therefore,a unifieddefinite algorithm for solving all these problems is given in this paper.During the procedure ofelimination,the unknowns are automatically separated into parameters and apparent variables.Thus,the freedom of the corresponding feedback can be defined as the number of parameters.Meanwhile,the explicit expressions of the apparent variables depending on the parameters areobtained.     

STRONG CONSISTENCY OF THE PERIODIC SMOOTHING SPLINES

Consider the regression model Y_i=u(x_i)+ε_i,i=1,2,…,n,where u(x)∈W_(2,per)~2[0,1],x_i=(i-1)/n,{ε_i}(?)are i.i.d,random variables.We use the periodic smoothing spline u_(λp)(x)toestimate u(x).Under certain conditions,strong consistency results of u_(λp)(x)are obtained,i.e.,forall 0相似文献   

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.     

POSITIVE SOLUTIONS FOR DIRICHLET PROBLEMS OF SINGULAR SEMILINEAR ELLIPTIC EQUATIONS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＤＩＲＩＣＨＬＥＴＰＲＯＢＬＥＭＳＯＦＳＩＮＧＵＬＡＲＳＥＭＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＣＵＩＳｈａｎｇｂｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓ...     

ALMOST PERIODIC SOLUTION FOR A CLASS OF LOTKA-VOLTERRA TYPE N-SPECIES ECOLOGICAL SYSTEMS WITH TIME DELAY

The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and new sufficient conditions are obtained for the global asymptotic stability of the unique positive almost periodic solution of the system.     

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…     

PERIODIC SOLUTIONS AND PERIOD-SIMILARITY OF A GROWTH MODEL WITH AGE-STRUCTURED POPULATION

The present paper deals with the periodic behaviours of an age-structured populationmodel.The period-similarity is proposed,which reveals a certain similar structure between thosepopulation models with distinct age structure.In addition,other results show that the fluctuations ofan age-structured population are closely related with the age structure.     

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

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

PERMANENCE AND PERIODIC SOLUTION IN AN INTEGRODIFFERENTIAL SYSTEM WITH DISCRETE DIFFUSION

Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.     

PERMANENCE AND PERIODIC SOLUTION OF NONAUTONOMOUS DELAY LOTKA-VOLTERRA DIFFUSION SYSTEM

1.IntroductionTheinfluenceofdiffusiononsystemdynamicalbehaviorhasbeenanAnportatsubjectofpopulationbiology.Morerealisticmodelsshouldincludesomeoftheststesofthesesystem,thatis,arealsystemshouldbemodeledbydmerelltialequationswithtimedelays.Kuanglllconsideredthepermanenceandpositiveperiodicsolutionofn-dimensionaldelayLotka-Volterracooperatesystem.Xiaoandafl2]discussedthepermanenceandpositiveperiodicsolutionofnonautonomous~ionLotforVolterracompetitivesystemsi.e.nit(t)=acfbi(t)--Zal,(t)xt] ZDti(…     

UPPER AND LOWER SOLUTIONS METHODS FOR EXISTENCE OF PERIODIC SOLUTIONS OF DUFFING EQUATION

1.IntroductionandNotationsInthispapertwestudytheexistenceofsolutionstothefollowingperiodicboundaryvalueproblemforthesecondorderDuffingequationwheresisarealparameter,g:[0,TIxR~RisaCarath6odoryfunctionandkER\{0}.Werecall(forexample,see[1])thatg:[0,TIxR~RiscalledaCarath6odoryfunctionifg(.,x)ismeasurableforallxERandg(t,.)iscontinuousfora.e.tE[0,TI.Theexistenceproblemfor(1.1)--(1.2)byusingtheupperandlowersolutionsmethodhasbeenstudiedbyFabryetal.in[2]foramoregeneralcasewhereacontinuousdampin…