一类抽象算子方程组的迭代解及其应用

在Banach空间中, 利用半序方法讨论了一类抽象算子方程组解的存在唯一性, 推广和统一了以前的一些结果. 然后应用到 Banach 空间非线性积分方程组, 得到了方程组的唯一解, 构造了收敛于方程组唯一解的迭代序列并给出了相应的误差估计.     

α-Bloch空间到H∞的加权复合算子

The article not only presents the boundedness and compactness of the weighted composition operator fromα-Bloch spaces(or littleα-Bloch spaces) to H~∞,but also gives some estimates for the norm of the weighted composition operator.     

单位球的Bergman空间上Schatten类加权复合算子

本文研究了单位球的Bergman空间上Schatten类加权复合算子,得到了这种加权复合算子属于Schatten-Von Neumann.理想S_p的几个充要条件.作为推论给出了Wφ,φ是一个Hilbert- Schmidt算子的充要条件是∫_(Bn)(|ψ(ω)|~2)/((1-|φ(ω)|~2)~(n 1)dV(ω)<∞..     

Existence Theorems for Set-valued Operators in Banach Spaces

In this paper, we study the problem of existence of zero points for set-valued operators in Banach spaces. We present a simple condition which can be used to verify that under some conditions, set-valued operators have zero points. Furthermore, we derive the surjectivity result and the Kakutani fixed point theorem by using this condition.      

混合单调算子的两点拉伸型不动点定理

本文首次提出了混合单调算子不动点的两点拉伸型条件.同时,利用锥映象的不动点指数理论建立了一类特殊的两点拉伸型混合单调算子的不动点存在性定理,并将所得结论应用于带有超线性项的积分方程与微分方程上,得到了新的结论.因而在本质上推进了混合单调算子不动点问题的研究.     

The L resolvents of elliptic operators with uniformly continuous coefficients

We consider the strongly elliptic operator A of order 2m in the divergence form with bounded measurable coefficients and assume that the coefficients of top order are uniformly continuous. For 1<p<∞, A is a bounded linear operator from the L^p Sobolev space H^m,p into H^−m,p. We will prove that (A−λ)⁻¹ exists in H^−m,p for some λ and estimate its operator norm.     

Weyl type theorems for operators satisfying the single-valued extension property

Let T be a bounded linear operator acting on a Banach space X such that T or its adjoint T^∗ has the single-valued extension property. We prove that the spectral mapping theorem holds for the B-Weyl spectrum, and we show that generalized Browder's theorem holds for f(T) for every analytic function f defined on an open neighborhood U of σ(T). Moreover, we give necessary and sufficient conditions for such T to satisfy generalized Weyl's theorem. Some applications are also given.     

Proximal methods in reflexive Banach spaces without monotonicity

We introduce the concept of hypomonotone point-to-set operators in Banach spaces, with respect to a regularizing function. This notion coincides with the one given by Rockafellar and Wets in Hilbertian spaces, when the regularizing function is the square of the norm. We study the associated proximal mapping, which leads to a hybrid proximal-extragradient and proximal-projection methods for nonmonotone operators in reflexive Banach spaces. These methods allow for inexact solution of the proximal subproblems with relative error criteria. We then consider the notion of local hypomonotonicity and propose localized versions of the algorithms, which are locally convergent.     

On the multistability of spatial solitons in waveguide and optical lattice

Properties of spatial solitons in channel waveguide and optical lattice are studied with the help of projection operator approach. The nonlinearity is assumed to be of cubic-quintic type. The stability consideration of the fixed point solutions of the ODE’s governing the evolution of soliton parameters indicates to the existence of more than one branch of soliton, giving rise to multistability. Explicit numerical analysis gives more information than the standard Vakhitov–Kolokov criterion. A systematic numerical simulation of the soliton profile gives detailed information about the nature of trapping and structure of the different branches of the pulse. It is observed that even under different launching conditions the solitons do not radiate but get trapped.     

Decay law for a quasistationary state of the Schrödinger operator for a crystal film

For the Schrödinger operator in a cell corresponding to a crystal film pattern, eigenvalues may exist in the continuous spectrum and become resonances under perturbations. We prove that the corresponding decay law in a nonstationary approach is exponential for a nondegenerate (in some cases, degenerate) eigenvalue.