涉及微分多项式的亚纯函数唯一性

本文研究了[fn(f-1)m](k)和[gn(g-1)m](k)分担1CM的唯一性问题,其中f和g为超越亚纯函数.此外,我们的定理在一定程度上推广了张晓宇等人的结果。     

闭极大线性子空间正交补的唯一性

研究赋范线性空间中闭极大线性子空间的正交可补性.利用空间的对偶映射给出固定闭极大线性子空间至多存在一个正交补的充分必要条件,从而给出每个闭极大线性子空间至多存在一个正交补的几何刻画.     

An Image Denoising-Deblurring Adaptive Variational Problem in BV Space

In this paper, we establish the existence and uniqueness of a BV solution to an initial boundary value problem for a nonlinear integro-differential equation, which is related to a denoising and deblurring variational model in image restoration. Several experiments relevant to the restoration model are performed and numerical results are discussed.     

A Fourth-order Degenerate Parabolic Equation with Variable Exponent

In this paper we establish the existence, uniqueness and long-time behavior of weak solutions for the initial-boundary value problem of a fourth-order degenerate parabolic equation with variable exponent of nonlinearity.     

一类非线性耦合双曲型方程组的研究

研究了一类非线性耦合双曲型方程组初边值问题,讨论了初边值条件以及非线性项中指数满足的条件,利用Galerkin方法和紧致性的结果,以及椭圆型方程解的正则性定理,经过严格的推导证明了该问题解的存在唯一性的若干结果.     

Some results on zeros and uniqueness of difference-differential polynomials

We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions.We also investigate the uniqueness problems of difference...     

A note on the existence of saddle points of p-th power Lagrangian for constrained nonconvex optimization

Li and Sun [D. Li and X.L. Sun, Existence of a saddle point in nonconvex constrained optimization, J. Global Optim. 21 (2001), pp. 39--50; D. Li and X.L. Sun, Convexification and existence of saddle point in a p-th-power reformulation for nonconvex constrained optimization, Nonlinear Anal. 47 (2001), pp. 5611--5622], present the existence of a global saddle point of the p-th power Lagrangian functions for constrained nonconvex optimization, under second-order sufficiency conditions and additional conditions that the feasible set is compact and the global solution of the primal problem is unique. In this article, it is shown that the same results can be obtained under additional assumptions that do not require the compactness of the feasible set and the uniqueness of global solution of the primal problem.     

The dynamic programming equation for stochastic optical control in hilbert spaces: a variational approach

The global existence of a point wise solution to the Hamilton-Jacobi equation for totally observed controlled diffusions in Hilbert spaces is proved by studying the corresponding control problem. The optimality principle for the control problem leads to local results, whilst an a priori bound is achieved by introducing a secondary minimization problem.     

A nonlocal problem with integral gluing condition for a third-order loaded equation with parabolic-hyperbolic operator involving fractional derivatives

This work devoted to prove of uniqueness and existence of solution of the nonlocal problem with integral gluing condition for the loaded parabolic-hyperbolic type equation involving Caputo derivatives which loaded parts in Riemann-Liouville integral-differential operator. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of integral equations.     

The Tychonoff uniqueness theorem for the G-heat equation

In this paper we shall investigate a uniqueness result for solutions of the G-heat equation. We obtain the Tychonoff uniqueness theorem for the G-heat equation.