共查询到20条相似文献,搜索用时 281 毫秒
1.
Qi Jiangang 《Annals of Differential Equations》2005,21(3):389-396
In this paper, we study a bounded-below singular Hamiltonian system. Sufficient and necessary conditions are obtained for the existence and the number of eigenvalues on the left-axis. The main results of this paper are the extension and improvement of Weyl spectral theorem for singular second order differential equations. 相似文献
2.
Tomasz Swiderski 《分析论及其应用》2011,27(2):167-180
In the present paper we study properties of Szász-Durrmeyer operators. These operators are introduced in [5] and generalize the integral operators proposed by S.M.Mazhar and V.Totik in [12]. We also generalize some results obtained by M. Heilmann[6] and D.-X. Zhou[16]. 相似文献
3.
In this note we study the property(ω),a variant of Weyl's theorem introduced by Rakoevic,by means of the new spectrum.We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property(ω) and approximate Weyl's theorem hold.As a consequence of the main result,we study the property(ω) and approximate Weyl's theorem for a class of operators which we call the λ-weak-H(p) operators. 相似文献
4.
In this paper, we propose an iterative method of approximating solutions for a class of the system of generalized variational inequalities and give a convergence result for the iterative method in uniformly convex and uniformly smooth Banach spaces. 相似文献
5.
We investigate a class of multilinear integral operators with the nonnegative kernels, and prove that the norms of the operators can be obtained by integral of the product of the kernel function and finitely many basic functions. Using the integral, we can easily calculate the sharp constants for the multilinear Hilbert inequality, the generalized Hardy-Littlewood-Sobolev inequality and the multilinear Hardy operator. 相似文献
6.
CHEN ChuanQiang 《中国科学 数学(英文版)》2013,56(3):639-651
In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations. 相似文献
7.
In the present paper we consider sequences of rational functions with a bounded number or free poles con-verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examinethe limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our resultsfurther extend the well known classical theory of overconvergence and the zeros of sections of Taylor series. 相似文献
8.
In this note we study the property (ω), a variant of Weyl's theorem introduced by Rakocevic, by means of the new spectrum. We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property (ω) and approximate Weyl's theorem hold. As a consequence of the main result, we study the property (ω) and approximate Weyl's theorem for a class of operators which we call the λ-weak-H(p) operators. 相似文献
9.
In this paper,we study an m-point boundary value problem of third order ODEs at resonance. We prove some existence results for the m-point boundary value problem at resonance by the coincidence degree theory of [8,9]. Our result is new. Meanwhile,an example is presented to demonstrate the main result. 相似文献
10.
In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions. 相似文献
11.
12.
In this paper, we give error estimates for the weighted approximation of r- monotone functions on the real line with Freud weights by Bernstein-type operators. 相似文献
13.
The (U + K)-orbit of a bounded linear operator T acting on a Hilbert space H is defined as (U + K)(T)={R-1 T R:R is invertible of the form unitary plus compact on H}.In this paper,we first characterize the closure of the (U + K)-orbit of an essentially normal triangular operator T satisfying H={ker(T-λI):λ∈ρ F (T)} and σ p (T*)=ф.After that,we establish certain essentially normal triangular operator models with the form of the direct sums of triangular operators,adjoint of triangular operators and normal operators,show that such operator models generate the same closed (U + K)-orbit if they have the same spectral picture,and describe the closures of the (U + K)-orbits of these operator models.These generalize some known results on the closures of (U + K)-orbits of essentially normal operators,and provide more positive cases to an open conjecture raised by Marcoux as Question 2 in his article "A survey of (U + K)-orbits". 相似文献
14.
Li Hongyu 《Annals of Differential Equations》2005,21(2):153-160
By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions, we prove the existence of positive solution of the problem. 相似文献
15.
We summarize several relevant principles for the application of abstract operators in partial differential equations, and combine abstract operators with the Laplace transform. Thus we have developed the theory of partial differential equations of abstract operators and obtained the explicit solutions of initial value problems for a class of higher-order linear partial differential equations. 相似文献
16.
In this paper, we define mean index for non-periodic orbits in Hamiltonian systems and study its properties. In general, the mean index is an interval in R which is uniformly continuous on the systems. We show that the index interval is a point for a quasi-periodic orbit. The mean index can be considered as a generalization of rotation number defined by Johnson and Moser in the study of almost periodic Schr?dinger operators. Motivated by their works, we study the relation of Fredholm property of... 相似文献
17.
Zeng Xiaoyun Shi Bao 《Annals of Differential Equations》2005,21(3):507-513
In this paper, we investigate the asymptotic behavior of the extremal solutions of a difference equation and their character and prove the existence of the non-extremal solutions. 相似文献
18.
19.
We present a definition of general Sobolev spaces with respect to arbitrary measures, Wh,p (Ω,μ) for 1 ≤p≤∞. In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cc∞ (R) is dense in thee spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials. 相似文献
20.
《分析论及其应用》1996,(1)
In this paper we Ointroduce linear-spaces consisting of continuous functions whose graphs are the attactars of a special class of iterated function systems. We show that such spaces are finite dimensional and give the bases of these spaces in an implicit way. Given such a space, we discuss how to obtain a set of knots for whah the Lagrange interpolation problem by the space is uniquely solvable. 相似文献