ALMOST PERIODIC SOLUTIONS OF NONLINEAR DUFFING'S EQUATIONS WITH DELAY

1Introduction:Recellt,lyIt.SchlniltandJa,nJ(lsit.Ward,JR.[l]developedamclfllo(1forestablishillgtheexistellceofalmostperiodicsolutionstonolllillcal'secorl'1order相似文献   

THE EXISTENCE OF ALMOST PERIODIC SOLUTIONS AND PERIODIC SOLUTIONS

In this paper,it is obtained that a periodic system has an almost periodic solution ifit has a solution x=(t)uniformly stable with respect to Ω_,and has a periodic solutionif x=(t)is weakly uniformly asymptotically stable with respect to Ω_.Meanwhile,it isalso obtained that a uniformly almost periodic system has an almost periodic solution if ithas a solution x=(t)uniformly asymptotically stable with respect to A_~f     

PERIODIC AND ALMOST PERIODIC SOLUTIONS OF A CERTAIN INFINITE DELAY INTEGRAL EQUATION

In this paper,by using successive approximation method and fixed-point theorem,we discuss a class of infinite delay integral equation and obtain some sufficient conditions which guarantee the existence and uniqueness of the peri- odic and almost periodic solutions of the system.     

SOME TOPOLOGICAL PROPERTIES ABOUT ALMOST PERIODIC DIFFERENTIAL EQUATIONS AND ALMOST PERIODIC SOLUTIONS

ＳＯＭＥ　ＴＯＰＯＬＯＧＩＣＡＬ　ＰＲＯＰＥＲＴＩＥＳ　ＡＢＯＵＴ　ＡＬＭＯＳＴ　ＰＥＲＩＯＤＩＣ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳ　ＡＮＤ　ＡＬＭＯＳＴ　ＰＥＲＩＯＤＩＣ　ＳＯＬＵＴＩＯＮＳＺｈａｎｇＪｉａｎｆｅｎｇ（张剑峰）（Ｆｕｚｈ...     

STABILITY AND ALMOST PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

ＳＴＡＢＩＬＩＴＹＡＮＤＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＮＥＵＴＲＡＬＴＹＰＥＹｕａｎＲｏｎｇ（袁荣）（ＢｅｉｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，北京师范大学，...     

RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS

This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,l) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.     

RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS

This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besov spaces B _r,r ⁶ (0.1) with 0<σ<∞ and (1+σ)⁻¹相似文献   

STABILITY AND EXISTENCE OF PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS ON LIENARD SYSTEMS

1MainResultsConsidersystem11~.x f(x)x' g(x)~0(1)wheref(x)islocallyintegrable,g(x)isdifferentiablealldg(0)=0.Theroem1Thezerosolutionofsystem(1)isuniformlyasymptoticallystableifbyequivalenttransf'Ormu=xov=X' F(x).DefineW[t,(uif\v)]j6ug(s)ds Iv',thenwisaposi…     

STABILITY AND ALMOST PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Itiswellknownthattheexistenceofalmostperiodicsolutionsiscloselyrelatedtothestabilityofsolutions.Forfunctionaldifferentialequationswithinfinitedelay,Y.Hin.[5'6]studiedtheproblemsontheexistenceofalmostperiodicsolutionsandthestability.However,therearefewpapersll2]dealingwithneutralfunctionaldifferentialequationswithinfinitedelay.Inthepresentpaper,forneutralfunctionaldifferentialequationswithinfinitedelay,weprovetheinherencetheoremfortheuniformlystableoperatorD(t),definethestabilitywithrespecttot…     

PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF THE SCALAR ORDINARY DIFFERENTIAL EQUATION

This paper develops a method which enables us to study the number,existence andstability of periodic solutions and almost periodic solutions of the scalar ordinarydifferential equation.Some applications of the method are also given.     

ON THE EXISTENCE OF PERIODIC SOLUTIONS OF NONLINEAR OSCILLATION EQUATIONS

This paper deals with the existence of periodic solutions of the nonlinear oscillationequation f(x)(x) ψ(x)η(x)=0.The author offers a method which can reduce(3)into the system=h(y)-e(y)F(x),=-g(x).(9)Some sufficient conditions for the existence of the limit cycles of(9)are obtained.These results generalize the results in [1,2,3,4,5,6](3)(9)obfained.     

THE EXISTENCE OF ALMOST PERIODIC SOLUTION TO NONLINEAR DIFFERENTIAL EQUATIONS

Ｃｏｎｓｉｄｅｒｎｏｎｌｉｎｅａｒａｌｍｏｓｔｐｅｒｉｏｄｉｃｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｘ＝Ａ（ｔ）ｘ（ｔ）＋ｆ（ｔ，ｘ（ｔ））（１）ａｎｄｉｔｓｈｏｍｏｇｅｎｅｏｕｓｌｉｎｅａｒｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｘ（ｔ）＝Ａ（ｔ）ｘ...     

BOUNDED SOLUTIONS AND PERIODIC SOLUTIONS OF VISCOUS POLYTROPIC GAS EQUATIONS

ＢＯＵＮＤＥＤＳＯＬＵＴＩＯＮＳＡＮＤＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＶＩＳＣＯＵＳＰＯＬＹＴＲＯＰＩＣＧＡＳＥＱＵＡＴＩＯＮＳＬＵＯＴＡＯＡｂｓｔｒａｃｔＡｐｉｓｔｏｎｐｒｏｂｌｅｍｏｆｖｉｓｃｏｕｓｐｏｌｙｔｒｏｐｉｃｇａｓｅｑｕａｔｉｏ...     

PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF A NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE AND DELAY

In this paper, by using the comparing theorem, Razumikhin-type theorem and V-function method, we consider a nonautonomous predator-prey system with stage-structure and time-delay. We get the sufficient conditions for the uniform persistence and the solutions global attractivity of this system. For a periodic system, we obtain the existence and uniqueness of a positive periodic solution of this system. For an almost periodic system, we prove the existence and the uniform asymptotic stability of the almost periodic solutions of this system.     

ON THE EXISTENCE OF ALMOST PERIODIC SOLUTIONS OF SOME DELAY DIFFERENTIAL EQUATIONS

By means of exponential dichotomy, this paper investigates the existence of almost periodic solutions of some delay differential equations.     

ON ALMOST PERIODIC SOLUTIONS OF AHIGHER ORDER ALMOST PERIODIC SYSTEM

1IntroductionConsiderthel'Ollowingdifferentialequationdx~~A(.t)x g(t,x),(l)dt.wherexeR",t6R,A(t)=(a,,(t)),,..istillnxncontinlloust'llllctiollmatrixinR,g(t,x)isanat-dimensionalcolltinuousfunctionvectorinRxR".Thepaper[l,21dealedwil;htheproblemontheexistence…     

ALMOST PERIODIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＰＩＥＣＥＷＩＳＥＣＯＮＳＴＡＮＴＡＲＧＵＭＥＮＴＹＵＡＮＲＯＮＧＨＯＮＧＪＩＡＬＩＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

THE NUMBER OF NONTRIVIAL SOLUTIONS TO HAMMERSTEIN NONLINEAR INTEGRAL EQUATIONS

In this paper,the author improves some results of Rabinowitz about the existence ofinfinitely many nontrivial solutions to Hammerstein nonlinear integral equations andgives some applications to the two-point boundary value problems for nonlinear ordinarydifferential equations.     

PERIODIC SOLUTIONS FOR A CLASS OF DELAYED NONLINEAR DIFFERENCE EQUATIONS

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree,some sufficient conditions are established for the global existence of positive periodic solutions of a class of delayed nonlinear difference equations.     

ALMOST PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONAUTONOMOUS OPERATOR

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＮＥＵＴＲＡＬＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＮＯＮＡＵＴＯＮＯＭＯＵＳＯＰＥＲＡＴＯＲ￥ＹＵＡＮＲＯＮＧ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｂｅｉ...