BOUNDEDNESS OF SOLUTIONS FOR SUPERLINEAR REVERSIBLE SYSTEMS

51. IntroductionThe boundedness problem of solutions of the following nonlinear scalar differelltial equa-nons of second order..x f(x, t)ic g(x, t) = 0 (1'1)has been widely investigated by many authors since the 1940's, where f(x, t 1) = j(x, t),g(x, t 1) = g(x, t).When j(x, t) = 0, Equation (1.1) is a conservative system and takes the following form..x g(x, t) ~ 0. (1'2)The first contribution of the boundedness of all the solutions of Equation (1.2) is due toMorrislll, whO proved …     

ON THE UNIFORM DISSIPATIVITY OF SOME FIFTH-ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

This paper studies the problem of uniformly dissipative solutions of somefifth order non-linear differential equations by the use of frequency domaintechnique. We use the generalized theorem of Yacubovich on dissipativity toobtain some new sufficient conditions of the existence of solutions that aredissipative for (1.1) and (1.2).     

具有足够大 Ginzburg-Landau参数的一维Ginzburg-Landau超导方程组对称解的唯一性

本文证明了：当Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ参数足够大时，一维Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ超导方程组的对称解 是唯一的．该问题的难点在于所考虑的解具有“奇点”：也即，当Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ参数趋于无穷大 时，解的导数在这些点处趋于无穷．证明的关键是要得到解在这些奇点近旁的精细估计．     

STRUCTURE OF POSITIVE SOLUTIONS OF A CLASS OF QUASILINEAR ORDINARY DIFFERENTIAL EQUATIONS

The existence and uniqueness of positive solutions for a class of quasilinearordinary differential equations with a large parameter are obtained. It is shownthat the flat core of positive solutions can exist. So some results of [1-3] aresharpened.     

SOME NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS FOR THIRD ORDER SINGULAR SUBLINEAR MULTI-POINT BOUNDARY VALUE PROBLEMS

We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x(3)(t) + f(t, x(t), x′(t)) = 0, 0 t 1,x(0)-m1∑i=1 αi x(ξi) = 0, x′(0)-m2∑i=1 βi x′(ηi) = 0, x′(1)=0,where 0 ≤ ai≤m1∑i=1 αi 1, i = 1, 2, ···, m1, 0 ξ1 ξ2 ··· ξm1 1, 0 ≤βj≤m2∑i=1βi1,J=1,2, ···, m2, 0 η1 η2 ··· ηm2 1. And we obtain some necessa βi =11, j = 1,ry and sufficient conditions for the existence of C1[0, 1] and C2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f(t, x, y)may be singular at x, y, t = 0 and/or t = 1.     

PERIODIC CHARACTER OF A DIFFERENCE EQUATION WITH MAXIMUM

We study the periodicity of the positive solutions of a class of difference equations with maximum. We prove that every positive solutions of these equations are eventually periodic.     

NONEXISTENCE OF PSEUDO-SELF-SIMILAR SOLUTIONS TO INCOMPRESSIBLE EULER EQUATIONS

In this paper we study a generalization of self-similar solutions. We show that just as for the solutions to the Navier-Stokes equations these supposedly singular solution reduce to the zero solution.In this paper we study a generalization of self-similar solutions. We show that just as for the solutions to the Navier-Stokes equations these supposedly singular solution reduce to the zero solution.     

两类方程亚纯解(n,1)级的上界估计

本文给出Riccati方程及另外一类具有代表性微分方程的亚纯解（n,1)级的上界估计，在一定条件下确立了文[2]中的猜测的正确性。     

BOUNDS FOR SOLUTIONS OF A THREE-POINT PARTIAL DIFFERENCE EQUATION

1IntroductionConsideraninitial-boundaryproblellll']oftileforulBylreansoftheforwardilltime-forwal'dillspacefillitedifferellcel-lletllodforcalculatillganapproximatesolutiollIL(nh,jk)=ALeofthisproblelll,weareledtotilefollowingdifferenceschemeoftheformwilerss=k/h.Suchallequationisaparticularcaseoftilefollowillggelleralpartialdifl'erellcewhere{hij},{oil}and{fti}arerealdollblesequellcesdefilledfori,j20.Itisclearthatiftilearegiven,thenwecancalculate'I[lo;till,liZ,o;u129'u21,'u3o;''successivelyill…     

非线性分数阶微分方程解的延拓

本文研究了分数阶微分方程(1.1)解的延拓问题.利用解的表达式给出方程解的可延拓条件,在此基础上研究了解可以延拓至何种程度的有关结果,且探讨了解的存在区间为[to,+∞)的条件.     

一类二阶非线性常微分方程解的有界性

本文研究了下列微分方程解的有界性，其中关于ｔ是１－周期的而关于ｘ是拟周期的．     

三维系统中一族闭轨在周期扰动下的分支

讨论一类三维系统在周期扰动下的分支问题.假设此三维系统有一族闭轨,利用 Poincar\'e映射及积分流形定理,得到了在周期扰动下由这族闭轨产生次调和解和不变环面的条件,并讨论了次调和解的鞍结点分支.     

一类微分方程组的非允许解

利用亚纯函数Nevanlinna的值分布理论，我们研究了一类代数微分方程组非允许解的存在性问题。并通过亏量δ(a，w)改进了非允许解的估计．     

关于超二次拉格朗日系统周期解的一个注记

证明了一类超二次的自治的Ｌａｇｒａｎｇｅ系统存在非平凡的周期解,并且如果相应的位势函数还是偶函数,那么这个系统拥有无穷多个周期解。     

THE MAXIMUM AND MINIMUM SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE WITH IMPULSES IN BANACH SPACES

ＴＨＥＭＡＸＩＭＵＭＡＮＤＭＩＮＩＭＵＭＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲ　ＩＮＴＥＧＲＯＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＭＩＸＥＤＴＹＰＥＷＩＴＨＩＭＰＵＬＳＥＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＬｉｕＷｅｉａｎ（刘伟安）（Ｗｕｈａｎ...     

EXISTENCE OF OSCILLATORY SOLUTIONS OF NEUTRAL DIFFERENTIAL EQUATIONS WITH "MAXIMA

1IntroductionInthispaperweconsiderthefollowingneutraldifferentialequationwherep9T)aarepositive,gEC(R ,R)andA7g(t)=oo,andfeC(R xR',R).WeshallassumethatthereexistsafunctionF(t,u,v)6C(R;,R )suchthatFisnondecreasinginuandvandWeshallnotethatequationswithmaximaoccurintheproblemofautomaticregulationofvariousrealsystems[4],[6].Themaximaariseswhentheregu-lationlawcorrespondstothemaximaldeviationoftheregurablequantity.Ourmaingoalwillbetoestablishsufficientconditionsfortheexistenceofoscillatorysol…     

一般状态空间马氏链随机泛函的指数矩

本文研究了一般状态空间马氏链随机泛函的指数矩.利用最小非负解理论,得到了随机泛函的指数矩是相应方程的最小非负解,推广了可数状态空间马氏链的结果,作为应用,证明了随机泛函的指数矩与漂移条件等价.     

Brusselator方程解的存在性和稳定性

本文研究了一种Brusselator方程的。用不变区域证明了解的全局存在性，并通过构造上下解给出了非常数定态解渐进稳定的条件。最后推出吸引域。     

关于双调和算子非线性基本方程正解的径向对称性

本文证明了双调和算子非线性基本方程的正解都是径向对称的，这些正解也是达到某类Ｓｏｂｏｌｅｖ最佳嵌入常数的采小元。     

EXTENDABILITY OF SOLUTIONS FOR THE LINEAR SYSTEM OF ELLIPTIC TYPE EQUATIONS

The solutions of linear system of elliptic type equations with first order isdiscussed by using the method of several complex analysis and, a series of newextended results of the solutions for the system of elliptic type are obtained.