中立型时滞差分方程有界正解的存在性

本文我们考察了中立型的滞差分方程Δ（ｘｎ－ｘｎ－ｋ）＋Ｐｎｘｎ－ｌ＝０ｎ＝０，１，２，…（＊）其中Ｐｎ（ｎ＝０，１，２，…）是正实数，ｋ和ｌ是非负整数．我们证明了：当且仅当则差分方程（＊）存在有界正解．     

ON MEROMORPHIC SOLUTIONS OF RICCATI AND LINEAR DIFFERENCE EQUATIONS

In this paper, meromorphic solutions of Riccati and linear difference equations are investigated. The growth and Borel exceptional values of these solutions are discussed, and the growth, zeros and pol...     

ON THE EXISTENCE OF PERIODIC SOLUTIONS OF NONLINEAR OSCILLATION EQUATION

This paper deal with the existence of periodic solutions of the nonlinear cscillation equation $$\[\mathop x\limits^{ \cdot \cdot } + f(x)\varphi (x) + \psi (x)\eta (x) = 0\begin{array}{*{20}{c}} {}&{(3)} \end{array}\]$$ The author offers a method which can reduce (3) into system $$\[\mathop x\limits^ \cdot = h(y) - e(y)F(x),\mathop y\limits^ \cdot = - g(x)\begin{array}{*{20}{c}} {}&{(9)} \end{array}\]$$ Some sufficient condition for the existence of the limit cycles of (9) are obtained. These results generalize the results in [1,2,3,4,5,6].     

ASYMPTOTIC BEHAVIOR AND EXISTENCE OF POSITIVE SOLUTIONS FOR A NEUTRAL DIFFERENCE EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｅｕｔｒａｌｄｉｆｅｒｅｎｃｅｅｑｕａｔｉｏｎ△（ｘｎ－ｃｘｎ－ｍ）＋ｐｎｘｎ－ｋ＝０，ｎ＝Ｎ，Ｎ＋１，Ｎ＋２，…，（１）ｗｈｅｒｅｃａｎｄｐｎａｒｅｒｅａｌｎｕｍｂｅｒｓ，ｋ，ｍａｒｅｐｏｓｉｔｉｖ...     

一类非线性差分方程存在正解的充分条件

本文得到具以下形式的非线性差分方程存在有界单增正解的充分条件△(rk(△yk-1)p-1)+skykp-1=0 (1)其中p＞1{rk}∞k=1为正数列,{sk}∞k=1是非负数列.     

THE PERIODIC SOLUTIONS OF RICCATIEQUATION WITH PERIODIC COEFFICIENTS

1IntroductionConsiderRiccatiequationwithperiodiccoefficientsZhaoHuaizhongin[21gavetwotheoremsTheorem1IfforA(x)20x6[0,ZT],1.If(2)isanidentityeverywhereforx6[0,Zr],theny=--B(x)/ZA(x)isaperiodicsolutionofequation(1)withperiodZT.2.Otherwise,thenequation(1)has…     

ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

In this paper, we present the properties on zeros, fixed points, poles, Borel exceptional value of finite order transcendental meromorphic solutions of complex difference equation of Malmquist typewhere n（∈ N） 〉 2, P（f（z）） and Q（f（z）） are relatively prime polynomials in f（z） with rational coefficients a8 （s = 0, 1,…,p） and bt （t = 0, 1,… ,q） such that aoapbq 7≠ O, and also consider the existence and the forms on rational solutions of this type of difference equations. Some examples are also listed to show that the assumptions of theorems, in certain senses, are the best possible.     

EXISTENCE OF ALMOST PERIODIC SOLUTIONS FOR DIFFERENCE SYSTEMS

1IntroductionAsisknown,therehavebeenquiteafewresu1tsontheexistenceofalrilostperiodicsolutionsforordinaryanddelaydifferentialstystems.However,tothebestofourknowledge,therehavenotappearedanycorrespondingresu1tsfOrevenordinarydifferencesystemssofar.Todealwithsuchproblems,wewilldefinethenotionoftheso-calleduni-formlyalmostperiodicsequencesbesidesthealmostsequencesandasymptoti-callyalmostsequences.Thenweprovidethecriteriaandthebasicpropertiesofuniformlyalmostperiodicsequenceswhichareneededinestabl…     

时滞Li

结合构造Liapunov泛函,研究了时滞Liénard方程概周期解的存在唯一性.     

强迫振动中周期解的存在性

本文主要研究了强迫振动方程：ｘ＋（ｆ（ｘ）＋ｇ（ｘ）ｘ）Ｘ＋ｈ（ｘ）＝ｅ（ｔ）的解的有界性以及周期解的存在性,这里ｆ（ｘ）,ｇ（ｘ）,ｈ（ｘ）在（－∞,＋∞）中连续,ｅ（ｔ）在「０,＋∞）上连续,得到了解的有界性与存在周期解的条件。     

THE EXISTENCE OF MULTIPLE SOLUTIONS OF p-LAPLACIAN ELLIPTIC EQUATION

1 IntroductionIn this paper we consider the following quasilinear elliptic problemwhere -- A. 'u = --div(l V ulp--' 7 u), A 2 0 is a real parametcr, 0 < m < p -- 1 < q < oc. flis a bounded domain in RN(N 2 3).During the last decade HLaplaJce equatiolls have e11jOyed a growing attention. After theinitial works of Poliozeav[1], and of Brezis and Nirenberg[2], there has been great number ofcontributious to the study of that kind of problem (1.1)A(see [3-161). Recently, equationiuvolving th…     

THE ANALYSIS OF EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR SECOND ORDER LINEAR SINGULAR DIFFERENTIAL DIFFERENCE EQUATION WITH DELAY

1IntroductionaccallthefollowingequationssingularfunctionaldifferentialequationsdenotedbySFDE.WhereAisanxmconstantmatrix,dctA=0whenn=m,x(t)ER",tEThebasictheoryofFDEhasbeenwellestablished.ComparedwithFDE,theSFDEismuchmorecofllplicated,whichisshowninthispaper.Inregardtothesingularsystemswithoutdelay,therearemailyresults.ButtherearefewresultsonSingularsystemswithdelay,andtherearcmanyinterestingproblemstobestudiedonthisclassofsystems.Peoplehavediscussedthelinearordinarydifferentialequation…     

高阶非线性差分方程的正解

本文讨论了一类奇数阶非线性中立型差分方程,获得了正解存在的充要条件和比较定理．     

POSITIVE PERIODIC SOLUTIONS OF NONLINEAR FUNCTIONAL DIFFERENCE EQUATION

Using the Krasnoselskii's fixed point theorem, the existence of positive periodic solutions to a class of nonlinear functional difference equations is studied in this paper. Some sufficient conditions for the existence of positive periodic solutions are presented.     

时滞差分方程周期正解的存在性

本文考虑了一类非线性离散种群模型周期正解的存在性.     

EXISTENCE OF POSITIVE SOLUTIONS AND 1/c-GLOBAL ATTRACTIVITY OF A NONLINEAR DELAY DIFFERENCE EQUATION WITH VARIABLE COEFFICIENTS

§ 1　IntroductionConsider the difference equationΔyn=rnynK -yn- ln K -cyn- ln,　 n =0 ,1 ,2 ,...,( 1 .1 )whereΔ is the forward difference operator defined byΔyn=yn+1 -yn,{rn}n≥ 0 is a sequenceof nonnegative real numbers,{ln}n≥ 0 is a sequence of positive integers,{n-ln}n≥ 0 is nonde-creasing,limn→∞ ( n-ln) =∞ ,and K is a positive constant,c∈ [0 ,1 ) .Obviously,( 1 .1 ) is aformally discrete analogue of the following single population growth model:N′( t) =r( t) N( t) K -N( t-τ( t…     

时滞Liénard方程概周期解的存在唯一性

结合构造Ｌｉａｐｕｎｏｖ泛函,研究了时滞Ｌｉｅｎａｒｄ方程概周期解的存在唯一性．     

ON THE EXISTENCE OF PERIODIC SOLUTIONS TO A CERTAIN FOURTH-ORDER NONLINEAR DIFFERENTIAL EQUATION

In this paper, we consider a certain fourth-order nonlinear ordinary differential equation. Some sufficient conditions which guarantee the existence of at least one ω-periodic solution to the system are obtain.     

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR SEMILINEAR HEAT EQUATION ON UNBOUNDED DOMAIN

In this paper, we consider the existence and nonexistence of global solutions to the semilinear heat equation ut - △u = u^p with Neumann boundary value δu/δv= 0 on some unbounded domains, where p &gt; 1, v is the outward normal vector on boundary δΩ. We prove that there exists a critical exponent Pc=Pc(Ω) &gt; 1 such that if p∈(1,pc], for nonnegative and nontrivial initial data, all positive solutions blow up in finite time; if p &gt; Pc, for suitably small nonnegative initial data, there exists a global positive solution.     

一类中立型泛函微分方程周期解问题

本文利用Fourier级数理论和Mawhin重合度拓展定理研究一类中立型泛函微分方程的周期解存在性问题.在其对应的特征方程具有零特征根的条件下,得到了周期解存在性的新结果.