Iterative Solution for Systems of Binary Non-mixed Monotone Operator Equations

With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATIONS

The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].

Iterative Solutions for a Non-monotone BinaryOperator Equations and Operator System of Equations

By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.

A Posteriori Parameter Choice Strategy for Nonlinear Monotone Operator Equations

In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ1/2) for Tikhonov-Browder regularization, where δ denotes the noise level of the data perturbation.

Fixed Point Theorems of Mixed Monotone Operators with Applications

In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.

Existence and Uniqueness of Fixed Points for Mixed Monotone Operators with Application

In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.

On Over-Relaxed Proximal Point Algorithms for Generalized Nonlinear Operator Equation with (A,η,m)-Monotonicity Framework

In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.

EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF PARABOLIC p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES

One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a（au/at）, studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2（O, T; L2 （Ω）） is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.

CONVERGENCE OF INVARIANT MEASURES FOR MULTIVALUED STOCHASTIC DIFFERENTIAL EQUATIONS

This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.

CONVERGENCE OF HYBRID VISCOSITY AND STEEPEST-DESCENT METHODS FOR PSEUDOCONTRACTIVE MAPPINGS AND NONLINEAR HAMMERSTEIN EQUATIONS

In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping （assuming existence） and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a non- linear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method.

带有分布时滞吊桥方程一致吸引子

考虑当依赖于时间的外力项平移有界而非平移紧时,内部反馈阻尼项含有分布时滞的以矩形板为模型的吊桥方程解的长时间动力学行为.首先,应用单调极大算子理论讨论了该方程解的适定性,进一步应用压缩函数方法证明过程族是一致渐近紧的,从而得到一致吸引子的存在性.

Convergence rates of regularized solutions of nonlinear ill-posed operator equations involving monotone operators

The convergence rates of regularized solutions of nonlinear ill-posed operator equations involving monotone operators are investigated, and conditions that guarantee convergence rates like $O(\delta ^{\frac{1}{2}} ),{\bf{ }}O(\delta ^{\frac{2}{3}} )$ and $O(\delta ^{\frac{n}{{n + 1}}} )$ are given, where δ denotes the noise level of the data perturbation.

一类单调二元算子方程组解的存在唯一性定理

利用锥理论和单调迭代技巧,得到了一类不满足连续性及紧性条件的非线性单调二元算子方程组解的存在唯一性及迭代逼近序列.

一类含参数分数阶微分方程边值问题正解的性质研究

研究了一类含参数的分数阶微分方程边值问题,主要运用锥上的不动点定理及混合单调算子特征值问题的性质得出了正解关于参数的性质:存在唯一性、单调性、连续性以及极限性质.最后举例说明了结果的可行性.

含有广义p-Laplace算子具混合边值条件的积分微分方程解的存在唯一性(英文)

本文研究了一类含有广义p-Laplace算子、具有混合边值条件的积分微分方程.运用将积分微分方程分解为非线性算子的研究方法,获得了这类方程解的存在唯一性的结论.与以往相关工作相比,不仅得到了解的存在性,还证明了解的唯一性.同时摒弃了传统的有限元法,而改用极大单调算子和伪压缩算子的值域理论研究问题,从而推广和补充了以往的研究工作.

一类Curvature方程的两种边值问题解的存在性

利用含有伪单调算子的变分不等式解的存在性定理,证明一类具有Dirichlet边值条件的Curvature方程在W1,p(Ω)空间中存在唯一解.深入研究具有Dirichlet边值条件的Curvature方程和具有Neumann边值条件的Curvature方程之间的关系,利用极大单调算子值域的扰动理论,给出具有Neumann边值条件的Curvature方程在W1,p(Ω)空间中存在解的充分条件.文中采用一些新的证明技巧,推广和补充了以往的相关研究成果.

奇异二阶脉冲微分方程边值正解的存在唯一性

利用混合单调算子不动点定理,研究有脉冲的二阶奇异微分方程Dirichlet边值问题,这里非线性项不仅对自变量可以是非奇异的,对函数也可以是奇异的。利用格林函数,将微分方程转化成等价解的积分方程,给出了该奇异非线性脉冲方程边值问题的正解的存在及唯一性的一个充分条件。最后举例说明所得到的结论。

一类非线性算子方程的最小最大耦合拟解的存在性(英文)

本文利用半序方法,研究了一类非线性算子方程的最小最大耦合拟解的存在性,得到几个新的存在性定理,并且改进和推广了[1-4]中相关结果.

L_p空间中Lipschitz强单调算子方程解的迭代算法

设E=L_p(1<p<∞),A:E→E~*为Lipschitz强单调算子.给出了L_p空间中Lipschitz强单调算子方程解的迭代构造算法,并证明由此算法构造的序列强收敛于A_x=0的唯一解,所得结果改进和推广了已有文献的相关结果.