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1.
熊晓蕾  谭冬妮 《数学学报》1936,63(6):629-638
设X和Y是赋范空间,如果映射f:X→Y满足{||f(x)+f(y)||,||f(x)-f(y)||}={||x+y||,||x-y||}(x,y∈X),则称f是一个相位等距算子.设g,f:X→Y是映射,若存在相位函数ε:X→{-1,1},使得ε·f=g,则称g和f是相位等价的.本文将证明改进的Tsirelson空间TM上的任意满相位等距算子均相位等价于一个线性等距算子.该结论同时也给出了改进的Tsirelson空间TM上的Wigner型定理.  相似文献   

2.
解析算子值函数的Riesz—Dunford积分   总被引:1,自引:1,他引:0  
1.引言 设H为复Hilbert空间,L(H)表示H上所有连续线性算子组成的Banach空间。若f(z)为定义在复平面区域D上的算子值函数,f(z)∈L(H)(z∈D),我们称f(z)于D上解析,是指对L(H)上的每个连续线性泛函φ,φ(f(z))为D上通常的复值解析函数,其全体记为A_H(D)。令  相似文献   

3.
在含p-laplacian算子的基础上,将多点边界条件与积分边界条件相结合,研究一类新的任意阶分数微分方程.通过求解等价积分方程,得到格林函数,再定义一个Banach空间中的连续算子,最后利用锥理论和不动点定理证明边值问题解的存在性,并通过实例验证所得结果的有效性.  相似文献   

4.
在弄清实函数连续点集结构的基础上,证明了不存在定义在R^n上的实函数f,使得f在有理点集Q^n上连续,而在无理点集(Q^n)上间断.并且得到:设(X,d)为具有σ有限开集的距离空间,E为X中的Gδ型集,则存在定义在X上的实函数f,使它在E上连续,而在F上间断.  相似文献   

5.
周志恒  韦煜明 《应用数学》2018,31(3):572-582
本文研究半无穷区间上具有共振的分数阶微分方程积分边值问题.通过构造适当的Banach空间及算子,利用迭合度理论和Mawhin连续性定理获得上述边值问题解的存在性结论,推广了前人的结果.  相似文献   

6.
共振情况下m点p-Laplacian算子边值问题解的存在性   总被引:4,自引:0,他引:4  
本文研究了在共振情况下m点P-Laplacian算子边值问题解的存在性问题.在非线性项f(t,u,v)有界的条件下,根据Mawhin的连续定理和m点P-Laplacian算子的边值问题的上下解理论,得出共振问题解的存在的结论.  相似文献   

7.
本文利用向量值H?lder连续函数空间C~α(R; X)上的算子值Fourier乘子定理,给出实轴上向量值分数阶时滞微分方程D~βu(t)=Au(t)+Fu_t+f (t), t∈R具有C~α-适定性的充分条件,其中A为某Banach空间X上的线性闭算子, F为从C([-r, 0]; X)到X的有界线性算子, r 0固定,函数u的t平移u_t定义为u_t(s)=u(t+s)(t∈R, s∈[-r, 0]),β 0固定, D~βu为函数u的β-阶Caputo导数.  相似文献   

8.
李冲  王兴华  张文红 《计算数学》2002,24(4):469-478
本文研究解决复合凸优化问题:min F(x):=h(f(x)) (P)x∈X的Gauss-Newton法的收敛性.这里f是从Banach空间X到Banach空间Y的具有Frechet导数的非线性映照,h是定义在Y上的凸泛函. 复合凸优化问题近年来一直受到广泛的关注,目前它已成为非线性光滑理论中的一个主流方向.它在非线性包含,最大最小问题,罚函数技巧 [1-5]等许多重要的问题和技巧中得到了广泛的应用.同时它也提供了一个新的统一框架,使优化问题数值解的理论分析得到别开生面的发展.并且它也是研究有限区域内一阶或二阶最优性条件的一个便利工具[3,5,6,7].  相似文献   

9.
研究了具有边界条件及转移条件的2n阶对称微分算子的特征值问题.首先构建了新的Hilbert空间使得所研究的微分算子在新的Hilbert空间中是自共轭的.然后利用微分算子谱分析经典方法,得到了λ是边值问题的特征值的充要条件,并给出了边值问题特征值的某些特点.  相似文献   

10.
本文首先利用由两组具有局部最小支集的样条所组成的基函数,构造非均匀2型三角剖分上二元三次样条空间S1,23(△(2)mn)的若干样条拟插值算子.这些变差缩减算子由样条函数B1ij支集上5个网格点或中心和样条函数B2ij支集上5个网格点处函数值定义.这些样条拟插值算子具有较好的逼近性,甚至算子Vmn(f)能保持近最优的三次多项式性.然后利用连续模,分析样条拟插值算子Vmn(f)一致逼近于充分光滑的实函数.最后推导误差估计.  相似文献   

11.
In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator of the form xa(x, x′)′. In this problem the maximal monotone term is required to be defined everywhere in the state space ℝN. The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ↦ (a(x)x′)′. In this case the maximal monotone term need not be defined everywhere, incorporating into our framework differential variational inequalities. Using techniques from multivalued analysis and from nonlinear analysis, we prove the existence of solutions for both problems under convexity and nonconvexity conditions on the multivalued right-hand side.  相似文献   

12.
非线性方程分歧理论中广义Lyapunov-Schmidt过程及应用   总被引:1,自引:0,他引:1  
本文讨论带有参数的算子方程 f ( x,λ) =0的分歧问题 ,其中 f :X×Λ→ Y,X,Y为 Banach空间 ,Λ =R为参数空间 .利用 A =f′x( x0 ,λ0 )的有界线性广义逆 A+ ,引入广义 Lyapunov-Schmidt过程 ,当 A为 Fredholm算子时 ,这种广义 Lyapunov-Schmidt过程就成为通常的 Lyapunov-Schmidt过程 .本文利用所引进的广义Lyapunov-Schmidt过程 ,证得关于抽象方程 f ( x,λ) =0的一个分歧定理 .  相似文献   

13.
Banach空间中拟线性投影算子   总被引:1,自引:1,他引:0  
证明了 :在自反 Banach空间$X$中 ,每个闭子空间 L,都存在 X到 L上的拟线性投影算子 SL.一般说来 ,SL 既非度量投影算子 ,又非线性算子 .  相似文献   

14.
姚庆六 《数学季刊》2008,23(1):61-66
By constructing suitable Banach space.an existence theorem is established under a condition of linear growth for the third-order boundary value problem u'"(t) f(t,u(t),t'(t),u"(t))=0,0<t<1,u(0)=u'(0)=u'(1)=0,where the nonlinear term contains first and second derivatives of unknown function.In this theorem the nonlinear term f(t,u,v,w)may be singular at t=0 and t=1.The main ingredient is Leray-Schauder nonlinear alternative.  相似文献   

15.
A STRONG RESONANCE PROBLEM   总被引:2,自引:1,他引:1  
Consider a functional f(x, v)=(Ax, x)/2+G(x, v), defined on a product space H×V. where H is a Hilbert space and V is a compact manifold. Suppose that the linear part (Ax, x) is at resonance. In this paper, the strong resonance problem is studied in the variational approach, the existence of at least, cuplength V+1 critical points of f is proved. The abstract theorems are then applied to the existence problems of solutions for elliptic boundary value problems and Hamiltonian systems.  相似文献   

16.
对非线性项f在py’= 0奇异但在y= 0非奇异的情形下,边值问题 正解的存在性作讨论.  相似文献   

17.
运用不动点指数理论,我们得到具有共振的二阶多点边值问题正解存在性的几个定理;其中的非线性项可以不连续.  相似文献   

18.
We consider a nonlinear operator equation with a Fredholm linear operator in the principal part. The nonlinear part of the equation depends on the functionals defined on an open set in a normed vector space. We propose a method of successive asymptotic approximations to branching solutions. The method is used for studying the nonlinear boundary value problem describing the oscillations of a satellite in the plane of its elliptic orbit.  相似文献   

19.
Let L^2([0, 1], x) be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2([0, 1], x) defined by a linear combination of Jo(μkX), where Jo is the Bessel function of order 0 and {μk} is the strictly increasing sequence of all positive zeros of Jo. For f ∈ L^2([0, 1], x), let E(f, n) be the error of the best L2([0, 1], x), i.e., approximation of f by elements of n. The shift operator off at point x ∈[0, 1] with step t ∈[0, 1] is defined by T(t)f(x)=1/π∫0^π f(√x^2 +t^2-2xtcosO)dθ The differences (I- T(t))^r/2f = ∑j=0^∞(-1)^j(j^r/2)T^j(t)f of order r ∈ (0, ∞) and the L^2([0, 1],x)- modulus of continuity ωr(f,τ) = sup{||(I- T(t))^r/2f||:0≤ t ≤τ] of order r are defined in the standard way, where T^0(t) = I is the identity operator. In this paper, we establish the sharp Jackson inequality between E(f, n) and ωr(f, τ) for some cases of r and τ. More precisely, we will find the smallest constant n(τ, r) which depends only on n, r, and % such that the inequality E(f, n)≤ n(τ, r)ωr(f, τ) is valid.  相似文献   

20.
In this paper we provide sufficient conditions for the existence of solutions to multipoint boundary value problems for nonlinear ordinary differential equations. We consider the case where the solution space of the associated linear homogeneous boundary value problem is less than 2. When this solution space is trivial, we establish existence results via the Schauder Fixed Point Theorem. In the resonance case, we use a projection scheme to provide criteria for the solvability of our nonlinear boundary value problem. We accomplish this by analyzing a link between the behavior of the nonlinearity and the solution set of the associated linear homogeneous boundary value problem.  相似文献   

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