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1.
本文在Bergman空间Bqp(p>0,q>1)中得到了关于用多项式逼近该空间函数的最佳逼近误差的阶的估计的逆定理.  相似文献   

2.
其中m,P,q>1.利用试验函数方法,首先推导一些积分不等式,然后对方程组爆破解的生命跨度 [0,T)给出估计.  相似文献   

3.
研究了平面上系数{Xn,n≥0}为(?)-混合序列在满足,(q>1)等条件下的随机级数的增长性及值分布,得到了比较好的结果.  相似文献   

4.
1IntroductionandMainResultsItiswellknownthatwhenp'--4q>0,secondorderautonomoussystemhastwocharacteristicexponentsfsothefollowingpropositionsareobvious.Proposition1Assumeq<0,then(1.1)hastwocharacteristicexponentswithoppositesigns.Proposition2Assumeq>0andp'…  相似文献   

5.
考虑一阶中立型方程 ., 云[z(£) 舻(c—r)] qx(c十f)一0,其中尹、q、f均为实常数,r>0,t>0. 方程(1)的特征方程是 △ ,(A)=A ?Ze一。 qe“=0. 引理1 方程(1)的所有解部振动的允要条件是特征方程(2)无实根[引.§l q>0的情形(2) 引理2特征方程(2)无实根的允要条件是对任意实数A有,(A)>0. 证明 充分性显然成立.只要证必要性,假如对任意实数A,,(A)>0不真,则有实数Ao,使,(A0)<0,而J.(0)一q>0,故在0与扎之M必仃,(A)一0的实根,矛盾. 定理I 方程(】)所有解振动的必要条件是p<0. 证明 只要证p≥0时方程(1)至少有一个非振动解.事实上,当p≥0时,l…  相似文献   

6.
二阶非线性微分方程组三点边值问题解的存在性   总被引:1,自引:0,他引:1  
利用上下解方法及Schauder不动点定理,证明了二阶非线性微分方程组三点边值问题: {y"=f(t,y,z,y',z') z"=g(t,y,z,y',z') y(-1)=A,y(1)=B,z(0)=C0,z'(0)=C1, 解的存在性,并由此得到四阶非线性微分方程三点边值问题解的存在性,一定程度上推广了前人的一些结果.作为文章结果的应用,讨论了奇摄动四阶半线性三点边值问题,得到该问题解的存在性及解的渐近估计.  相似文献   

7.
一类半线性热方程整体解的存在性与非存在性   总被引:3,自引:0,他引:3  
刘亚成  杨海欧 《数学学报》1999,42(2):321-326
本文研究半线性热方程的初值问题u_t-△u=u~γ+cu,(γ>1);u(x,0)=(x)非负整体L~P解的存在性与非存在性.首先证明,若C>0,则不存在非负整体解.而后,对C<0情形给出了解的整体存在与非存在的充分条件,特别证明了,若P>(γ一1)或,则当。充分小时存在非负整体L~P解.最后,对系数C和初值(x)得到无穷多个门槛结果.  相似文献   

8.
冯育强 《应用数学》2007,20(3):473-477
本文关注如下的二阶隐式微分方程f(t,u(t),u″(t))=0,a.e.t∈(O,1),边值条件为u(0)=u(1)=0.利用上下解方法和迭代技巧研究了该问题的可解性并得到了一些解的存在性结果.  相似文献   

9.
Activator—Inhibitor模型的古典整体解   总被引:1,自引:0,他引:1  
Gierer,Meinhardt提出了反映生物模式形成的Activator-Inhibitor模型其中u(x,t),v(x,t)分别表示Activator,Inhibitor的分布,d,D,μ,v是正常数,σ是非负常数,p>1,q>0,r>0,s≥0且满足0<(p-1)/q 相似文献   

10.
考察了动态M/G/1排队系统问题.利用泛函分析中的C0-半群理论给出了系统非负解的存在唯一性.  相似文献   

11.
矩阵方程X—A*X~qA=I(0<q<1)Hermite正定解的扰动分析   总被引:1,自引:1,他引:0  
高东杰  张玉海 《计算数学》2007,29(4):403-412
首先证明了非线性矩阵方程X-A~*X~qA=I(0相似文献   

12.
研究二次矩阵方程X2-bX-C=O(b>0,C为n×n阶正定阵)的正定解,证明了解的存在唯一性并且给出了求解方法.  相似文献   

13.
Nonlinear matrix equation Xs + AXtA = Q, where A, Q are n × n complex matrices with Q Hermitian positive definite, has widely applied background. In this paper, we consider the Hermitian positive definite solutions of this matrix equation with two cases: s ? 1, 0 < t ? 1 and 0 < s ? 1, t ? 1. We derive necessary conditions and sufficient conditions for the existence of Hermitian positive definite solutions for the matrix equation and obtain some properties of the solutions. We also propose iterative methods for obtaining the extremal Hermitian positive definite solution of the matrix equation. Finally, we give some numerical examples to show the efficiency of the proposed iterative methods.  相似文献   

14.
李静  张玉海 《计算数学》2008,30(2):129-142
考虑非线性矩阵方程X-A*X-1A=Q,其中A是n阶复矩阵,Q是n阶Hermite正定解,A*是矩阵A的共轭转置.本文证明了此方程存在唯一的正定解,并推导出此正定解的扰动边界和条件数的显式表达式.以上结果用数值例子加以说明.  相似文献   

15.
Bergman空间B_q~p(p>0,q>1)中的Bernstein型不等式   总被引:1,自引:1,他引:0  
邢富冲 《数学学报》2006,49(2):431-434
本文在Bergman空间Bqp(p>0,q>1)中得到了关于用多项式本身的模控制其导函数的模的Bernstein型不等式.  相似文献   

16.
§ 1 IntroductionLetRn×mdenotetherealn×mmatrixspace ,Rn×mr itssubsetwhoseelementshaverankr ,ORn×nthesetofalln×northogonalmatrices,SRn×n(SRn×n≥ ,SRn×n>)thesetofalln×nrealsymmetric (symmetricpositivesemidefinite ,positivedefinite)matrices.ThenotationA>0 (≥ 0 ,<0 ,≤ 0 )m…  相似文献   

17.
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^*X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.  相似文献   

18.
本文讨论如下内容:1.把有关对称正定(半正定)的一些性质推广到广义正定(半正定)。2.给定x∈Rm×m,∧为对角阵,求AX=x∧在对称半正定矩阵类中解存在的充要条件及一般形式,并讨论了对任意给定的对称正定(半正定)矩阵A,在上述解的集合中求得A,使得  相似文献   

19.
Matrix orthogonal polynomials whose derivatives are also orthogonal   总被引:2,自引:2,他引:0  
In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove that the corresponding orthogonality matrix functional is characterized by a Pearson-type equation with two matrix polynomials of degree not greater than 2 and 1. The proofs are given for a general sequence of matrix orthogonal polynomials, not necessarily associated with a hermitian functional. We give several examples of non-diagonalizable positive definite weight matrices satisfying a Pearson-type equation, which show that the previous results are non-trivial even in the positive definite case.A detailed analysis is made for the class of matrix functionals which satisfy a Pearson-type equation whose polynomial of degree not greater than 2 is scalar. We characterize the Pearson-type equations of this kind that yield a sequence of matrix orthogonal polynomials, and we prove that these matrix orthogonal polynomials satisfy a second order differential equation even in the non-hermitian case. Finally, we prove and improve a conjecture of Durán and Grünbaum concerning the triviality of this class in the positive definite case, while some examples show the non-triviality for hermitian functionals which are not positive definite.  相似文献   

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