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1.
§1. IntroductionRecently,thesemilinearellipticequations△u+f(u)=0(1.1)u(x)→0as|x|→∞(1.2)inRnwereconsideredwidely(see[1]-[7]).Inthenicepapers[1]and[2],itwasprovedthatanypositivesolutionof(1.1)mustberadialincasef(u)∈C1+δ(δ>0).Therefore,anypositivesoluti…  相似文献   

2.
王书彬  吕延华 《数学季刊》1998,13(3):102-110
§1. IntroductionIn[1,2],AronsonandWeinbergerhavestudiedsystematiclythescalarnonlineardiffu-sionequationinonespacevariableut=uxx+φ(u),(1.1)whereu=u(x,t)andφ(u)isanonlinearfunction.Equation(1.1)arisesinseveralapplica-tions;See[1,2]and[3]forinformationa…  相似文献   

3.
§1. IntroductionTheexistencefortheboundaryvalueproblemshavebeenwidelystudiedrecently.Inthispaper,wewilldiscusstheBVPofthefollowingconditions:u(n)+a(t)f(u)=0,0<t<1,u(k)(0)=0,0kn-2(1.1)u(1)=0, where(h1)a:(0,1)→(0,∞)isacontinuousfunction.(h2)f:[0,∞)→[…  相似文献   

4.
§1. IntroductionIn1908,E.Landauintroducedthefollowingwellknownsequenceofoperators[1]Ln[f(t);x]=Kn∫1-1f(t)[1-(t-x)2]ndt,    (1.1)where     Kn=[∫1{-1(1-t2)ndt]-1~nπ  (n→∞).(1.1)wasusedintheproofoftheWeierstrassTheorem.Sincethen,theapproximationprop-ert…  相似文献   

5.
郑学良 《数学季刊》1998,13(4):29-32
§1. IntroductionandNarratationoftheTheoremIffunctionfisanalyticindomainDandf′(z)≠0atpointz,wedefinetheschwarzianderivativeoffasSf(z)=(f″(z)f′(z))′-12(f″(z)f′(z))2.(1.1)  Foralocallyunivalentholomorphicfunction,itsSchwarzianderivativeisclear.Atpoles,t…  相似文献   

6.
1IntroductionConsiderthesecondorderordinarydiferentialequationx″+q(t)x=0,t≥0.(1.1)SupposethatQ(t)=∫+∞tq(s)ds(1.2)converges(po...  相似文献   

7.
§1. IntroductionNowadays,theresearchoftheinfintedelayfunctionaldifferentialquationhasdevelopeddeeply.Manyliteratureshavebeenconcernedforresearchtheintegraldifferentialquationasfollowsx(t)=-a(t)x(t)+∫t-∞k(t,s-t,x(s))ds.(1)  Inordertostudytheinfinited…  相似文献   

8.
Boundary Extension of μ(z)—homeomorphism   总被引:1,自引:0,他引:1  
郑学良 《数学季刊》1999,14(2):94-96
§1. IntroductionItiswellknownthattheBeltramiequationfz=μ(z)fz(1.1)hasauniquehomeomorphicsolutionundernormalizationconditionwhenyμ(z)y∞<1.Thissolutionishabituallycalledaquasiconformalmappingwithcomplexdilatationμ(z)[1].Withoutthisessentialrestriction…  相似文献   

9.
数形结合(续完)晨旭例25(1986年理科)当x∈[-1,0]时,下面关系式正确的是()(A)π-arccos(-x)=arcsin1-x2.(B)π-arcsin(-x)=arccos1-x2.(C)π-arcosx=arcsin1-x2.(D)π...  相似文献   

10.
1IntroductionandtheResultConsideraplanaranalyticsystemoftheformx=P(x,y),y=Q(x,y),(1.1)wherePandQareanalyticfunctionsin(x,y)in...  相似文献   

11.
An operator is essentially subnormal if its image in the Calkin algebra is subnormal. We shall characterize the essentially subnormal operators as those operators with an essentially normal extension. In fact, it is shown that an essentially subnormal operator has an extension of the form ``normal plus compact'.

The essential normal spectrum is defined and is used to characterize the essential isometries. It is shown that every essentially subnormal operator may be decomposed as the direct sum of a subnormal operator and some irreducible essentially subnormal operators. An essential version of Putnam's Inequality is proven for these operators. Also, it is shown that essential normality is a similarity invariant within the class of essentially subnormal operators. The class of essentially hyponormal operators is also briefly discussed and several examples of essentially subnormal operators are given.

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12.
The authors characterize the (μ +κ)-orblts of a class essmntially normal operators and provethat some essentially normal operators with connected spectrum are strongly irreducible aftera small compact perturbation. This partially answers a question of Domigo A. Herrero.  相似文献   

13.
We characterize the essentially normal composition operators induced on the Hardy space H2 by linear-fractional maps; they are either compact, normal, or (the nontrivial case) induced by parabolic nonautomorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition, we characterize those linear-fractionally induced composition operators on H2 that are essentially self-adjoint, and present a number of results for composition operators induced by maps that are not linear-fractional.  相似文献   

14.
In this paper an easier proof is obtained of Alexandru Aleman's extension of an inequality of Axler and Shapiro for subnormal operators to the essential norm. The method is applied to show that a hyponormal operator whose essential spectrum has area zero must be essentially normal.

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15.
在本文中 ,我们给出了一类本质正规算子的稳定不变子空间的特征 .即 ,T∈ L( H2 ( Ω;μ) )且满足1 ) T是本质正规算子 ;2 )σ( T) =Ω,σe( T) = Ω,σp( T) =Ω ;3) ind( T-z) =n,z∈Ω;4 ) minind( T-z) =0 ,z∈ Ω.M是 T的非平凡的不变子空间 ,则 M是 T的稳定不变子空间当且仅当 dim M<∞ and dim M⊥ =∞  相似文献   

16.
于涛  程国正 《数学学报》2007,50(5):1007-101
在单位多圆盘的Bergman空间上,本文分别刻画了以有界可测函数和有界多重调和函数为符号的本质交换对偶Toeplitz算子.  相似文献   

17.
The idea of symmetric anti-eigenvalue and symmetric anti-eigenvector of a bounded linear operator T on a Hilbert space H is introduced. The structure of symmetric anti-eigenvectors of a self-adjoint and certain classes of normal operators is found in terms of eigenvectors. The Kantorovich inequality for self-adjoint operators and bounds for symmetric anti-eigenvalues for certain classes of normal operators are also discussed.  相似文献   

18.
本文利用BDF定理以及构造技巧证明了关于本质正规算子的Pearcy-Salinas定理.作为此定理的应用,证明了本质正规算子可以通过迹类算子的小扰动成为不可约算子.  相似文献   

19.
Quasidifferentials are studied with the theory of maximal normal operators. The quasidifferential of a normally quasidifferentiable function is a pair of upper and lower semicontinuous operators, which are special maximal normal operators. The function sum of the upper and lower semicontinuous operators is the Clarke subdifferential of this function. Basic calculus and minimal forms of quasidifferentials are also discussed.  相似文献   

20.
本文讨论多圆盘上Bergman空间上的具有多重调和符号的Toeplitz算子的本质可换性与可换性.我们获得了一个解析或共轭解析Toeplitz算子与具有多重调和符号的Toeplitz算子本质可换的充分必要条件是它们是可换的.  相似文献   

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