非Lipschitz系数下随机泛函微分方程适度解的存在唯一性及其渐近性态(英文)

本文主要运用Picard迭代和算子分数次幂方法,讨论了随机时滞偏微分方程适度解的存在性与唯一性,并对解的渐近性态进行了研究.这里方程的系数不满足Lipschitz条件,时滞r>0为有限的.最后给出了一个非Lipschitz条件的例子.     

非全局Lipschitz条件下随机延迟微分方程Euler方法的收敛性

大多数随机延迟微分方程数值解的结果是在全局Lipschitz条件下获得的.许多延迟方程不满足全局Lipschitz条件,研究非全局Lipschitz条件下的数值解的性质,具有重要的意义.本文证明了漂移系数满足单边Lipschitz条件和多项式增长条件,扩散系数满足全局Lipschitz条件的一类随机延迟微分方程的Eul...     

非Lipschitz系数随机波动方程适度解的存在唯一性

本文在系数为非Lipschitz条件下(Lipschitz和线性增长作为其特例),通过构造逐次逼近列的方法证明了随机波动方程适度解的存在唯一性.     

非Lipschitz条件下高维McKean-Vlasov随机微分方程解的存在唯一性

研究了一类漂移系数不连续的高维McKean-Vlasov随机微分方程及相应的粒子系统解的存在唯一性.在漂移系数关于空间变量逐段Lipschitz连续的条件下，首先利用Zvonkin变换将方程转换为漂移系数为Lipschitz连续的McKean-Vlasov随机微分方程，变换后的方程存在唯一解.然后由变换函数的性质可得逆函数的存在性和Lipschitz连续性.最后由It8公式及逆函数的性质可得原来的McKean-Vlasov随机微分方程及相应的粒子系统解的存在唯一性.     

一类具有Lipschitz条件的非线性映象的迭代过程

使用新的分析技巧,讨论了Lipschitzφ-强增生算子方程的解和Lipschitzφ-强伪压缩映象不动点的迭代逼近问题.改进和推广了Chang,Chidume,Deng-Ding,Deng,Tan-Xu和Osilike等人的相关结果.     

关于增生算子方程解的Ishikawa迭代逼近

设X是任意实Banach空间,T:X→X是Lipschitz连续的增生算子.本文证明了,带误差的Ishikawa迭代序列强收敛到方程x Tx=f的唯一解.而且,还给Ishikawa迭代序列提供了一般的收敛率估计.利用该结果,本文推得,若T:X→X是Lipschitz连续的强增生算子,则带误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解.     

Lévy过程驱动的随机发展方程的几乎自守解（英文）

本文介绍了泊松p-期望几乎自守随机过程的概念,在非Lipschitz条件下给出了泊松p-期望几乎自守函数的一个分解定理;在此基础上,运用所得结果研究了一类由Lévy过程驱动的随机发展方程,给出了此类方程均方几乎自守解存在的充分条件并举例说明所得结果的有效性.     

具有非Lipschitz系数的多值随机发展方程

本文在发展三元组的框架下,研究了一种具有极大单调算子和非Lipschitz系数的多值随机发展方程.在一定条件下,我们证明了这种方程的解的存在唯一性.     

增生算子方程的具误差的Ishikawa迭代序列的强收敛定理

本文研究了Banach空间中Lipschitz的增生算子T的方程的解的迭代逼近问题.利用Ishikawa迭代法,证明了具误差的Ishikawa迭代序列强收敛到方程的唯一解,得到了一般的收敛率估计式.     

Banach空间中关于增生算子方程的迭代法的强收敛定理

设X是一实Banach空间,且TX→X是Lipschitz连续的增生算子.在没有假设lim αn=1imβn=0之下,本文证明了,Ishikawa迭代序列强收敛到方程x+Tx=f的唯一解,而且还对Ishikawa迭代序列提供了一般的收敛率估计.利用该结果,我们推得,当TX→X是Lipschitz连续的强增生算子时,Ishikawa迭代序列强收敛到方程Tx=f的唯一解.     

Lipschitz Regularity in Some Geometric Problems

The Lipschitz regularity is perhaps the most natural, and surely the most geometrical among all the types of regularities. For example, the Lipschitz character of an ordinary differential equation (vector field) is the natural classical sufficient condition for the (unique) integrability of this equation. The goal here is to show that, in some sense, the Lipschitz regularity is also necessary, if one assumes (geometric) individual conditions on the trajectories. In other words, we show that tangential rigidity leads to a transversal regularity.     

Inertial Manifolds for Weakly and Strongly Dissipative Hyperbolic Equations

One considers mixed boundary value problems for a quasilinear hyperbolic equation with a weak, as well as strong, dissipation. The nonlinear function in the equation is assumed Lipschitz continuous. For each of these problems one obtains the conditions on the Lipschitz constant that ensure the existence of inertial manifolds.     

Existence and uniqueness theorem for uncertain differential equations

Canonical process is a Lipschitz continuous uncertain process with stationary and independent increments, and uncertain differential equation is a type of differential equations driven by canonical process. This paper presents some methods to solve linear uncertain differential equations, and proves an existence and uniqueness theorem of solution for uncertain differential equation under Lipschitz condition and linear growth condition.     

满足递推式紧集的Lipschitz等价性

设紧集U满足一个不交并递推式,U=(rU+(?))∪U_1.证明了若U_1与一个满足强分离条件的自相似集T Lipschitz等价,则U与T也是Lipschitz等价.并举例说明定理在自相似并集间的Lipschitz等价中的应用.     

Cosmically Lipschitz Set-Valued Mappings

This paper introduces a kind of sub-Lipschitz continuity for set-valued mappings based on the cosmic metric. This type of Lipschitz behavior has applications with regards to necessary optimality conditions, the Hamilton–Jacobi equation, and invariance of unbounded differential inclusions. Cosmically Lipschitz assumptions allow for broader applications than previously allowed under Lipschitz assumptions. It is also shown that a cosmically Lipschitz mapping can be characterized by the normal cones to its graph using the coderivative, and various rules are presented in order to more easily identify such a mapping.     

Convergence of Rothe's method for fully nonlinear parabolic equations

Convergence of Rothe's method for the fully nonlinear parabolic equation u_t+F(D²u, Du, u, x, t)=0 is considered under some continuity assumptions on F. We show that the Rothe solutions are Lipschitz in time, Hölder in space, and they solve the equation in the viscosity sense. As an immediate corollary we get Lipschitz behavior in time of the viscosity solutions of our equation.     

由Lévy过程驱动的反射型倒向随机微分方程

证明了由Lévy过程驱动的反射型倒向随机微分方程在局部Lipschitz系数下的解的存在唯一性,并且研究了解的稳定性质.此外,当系数满足Lipschitz条件以及反射壁正则时,证明了过程K的正则性.     

关于增生算子方程解的带误差的Ishikawa迭代程序

该文在Banach空间中证明了，带误差的Ishikawa迭代序列强收敛到Lipschitz连续的增生算子方程的唯一解．而且，也给Ishikawa迭代序列提供了一般的收敛率估计．利用该结果还推得，带误差的Ishikawa迭代序列也强收敛到Lipschitz连续的强增生算子方程的唯一解．     

On approximate solution of stochastic delay evolution equation in infinite dimensions

In [6] [7], the coefficients of given equation are supposed to be Lipschitz continuity or to be a bit weaker than Lipschitz continuity for establishing existence and uniqueness of the solution. In this paper, we show that, under the assumption of so-called pathwise uniqueness to the equation, a weaker restriction to coefficients than these mentioned above will recapture the convergence of Carathéodory approximation of the equation in the strong sense.     

Lipschitz continuity for solutions of the ᾱ-Poisson equation

In this paper, we study the Lipschitz continuity for solutions of the ?-Poisson equation. After characterizing the boundary conditions for the Lipschitz continuity of ?-harmonic mappings, we present four equivalent conditions for the(K, K′)-quasiconformal solutions of the ?-Poisson equation with a nonhomogeneous term to be Lipschitz continuous.