A surjectivity result for quasibounded operators

Using a degree theory for countably 1-contractive operators, we show a surjectivity theorem for such quasibounded operators. Moreover, the existence of an eigenvalue for these operators is presented.     

The Leray–Schauder approach to the degree theory for -perturbations of maximal monotone operators in separable reflexive Banach spaces

The purpose of this paper is to demonstrate the fact that the topological degree theory of Leray and Schauder may be used for the development of the topological degree theory for bounded demicontinuous (S₊)-perturbations f of strongly quasibounded maximal monotone operators T in separable reflexive Banach spaces. Certain basic homotopy properties and the extension of this degree theory to (possibly unbounded) strongly quasibounded perturbations f are shown to hold. This work uses the well known embedding of Browder and Ton, and extends the work of Berkovits who developed this theory for the case T=0. Besides being an interesting mathematical problem, the existence of such a degree theory may, conceivably, become useful in situations where the use of the Leray–Schauder degree (via infinite dimensional compactness) is necessary.     

The spectral remainder estimates for non-isotropic polyharmonic operators on bounded and quasibounded domains

Summary Approximation numbers of the embedding operator of the nonisotropic Sobolev space W^(m), 2(Q) into L²(Q), Q being an n-dimensional open box, are applied to the study of spectral asymptotics. We deal with the nonisotropic polyharmonic operators on bounded and quasibounded open sets in Rⁿ. The quasibounded open sets are required to satisfy theG _k,a ^(m),2 -condition. Not only the leading terms of the asymptotic formulae but also remainder terms are obtained. An application is made to a quasibounded domain whose width has a negative power-type decay at infinity.     

一类非线性算子的耦合不动点定理及其应用

本文定义了斜增算子及其耦合不动点，利用扩展算子的方法证明了斜增算子的耦合不动点定理，并给出了迭代公式。     

拟序下非连续增算子新的广义不动点定理

运用序方法研究了拟序空间X中具A=CB型非连续增算子的广义不动点的存在性问题,证明了在拟序空间X中具A=CB型非连续增算子存在最小广义不动点和最大广义不动点.所得结果推广了相关结论.     

On a fixed point theorem for the product of operators

In this paper, we study the existence of fixed points for the product of nonlinear operators. This kind of fixed point theorems is necessary in consideration of quadratic differential and integral problems. We emphasize a possible extension of the applicability of obtained theorems and consequently we prove the existence of fixed points for operators acting on some function spaces that are not necessarily Banach algebras. This result can be successfully applied to many quadratic problems.     

On random fixed point theorems of random monotone operators

In this paper, we investigate the existence of random fixed point for random mixed monotone operators and random increasing (decreasing) operators and obtain some new random fixed point theorems.     

Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming

In this paper, the existence and iterative approximation of coupled fixed points for mixed monotone condensing (set-valued) operators are discussed. The results presented here extend and improve the corresponding results of [D. Guo and V. Lakshmikantham, coupled fixed points of nonlinear operators [1, 2]. As an application, we utilize the results obtained in Section 2 to study the existence problem of solutions for a class of functional equations arising in dynamic programming.     

Noncompact‐type Krasnoselskii fixed‐point theorems and their applications

In this paper, we first establish some user‐friendly versions of fixed‐point theorems for the sum of two operators in the setting that the involved operators are not necessarily compact and continuous. These fixed‐point results generalize, encompass, and complement a number of previously known generalizations of the Krasnoselskii fixed‐point theorem. Next, with these obtained fixed‐point results, we study the existence of solutions for a class of transport equations, the existence of global solutions for a class of Darboux problems on the first quadrant, the existence and/or uniqueness of periodic solutions for a class of difference equations, and the existence and/or uniqueness of solutions for some kind of perturbed Volterra‐type integral equations. Copyright © 2015 John Wiley & Sons, Ltd.     

Fixed point theorems for mixed monotone operators with perturbation and applications to fractional differential equation boundary value problems

The purpose of this paper is to present some new fixed point theorems for mixed monotone operators with perturbation by using the properties of cones and a fixed point theorem for mixed monotone operators. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.     

一类时滞依赖状态的集值抽象积分微分方程的可解性

本文研究了一类时滞依赖状态的集值抽象积分微分方程的可解性问题.利用集值映射不动点定理结合分析预解算子理论的方法,证明了上述微分方程温和解的存在性,推广了现有集值微分方程的结果.     

FIXED POINTS AND COUPLED FIXED POINTS FOR INCREASING OPERATORS WITH APPLICMIONS TO DIFFERENTIAL INCLUSIONS IN BANACH SPACES

ＦＩＸＥＤＰＯＩＮＴＳＡＮＤＣＯＵＰＬＥＤＦＩＸＥＤＰＯＩＮＴＳＦＯＲＩＮＣＲＥＡＳＩＮＧＯＰＥＲＡＴＯＲＳＷＩＴＨＡＰＰＬＩＣＭＩＯＮＳＴＯＤＩＦＦＥＲＥＮＴＩＡＬＩＮＣＬＵＳＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＺＨＡＮＧＳＨＩＳＨＥＮＧＡＮＤＨＵ...     

Banach空间中半闭1-集压缩算子的不动点定理及其应用(英文)

本文通过定义在Menger-PN的算子建立不同的边界条件,考虑半闭1-集压缩算子的不动点的存在性问题,得到了半闭1-集压缩算子的一些不动点定理.本文中所采用的方法与相关文献中的方法完全不同.     

Existence theorems for monotone operators in reflexive Banach spaces

In this paper, we obtain an existence theorem for single-valued monotone operators in a reflexive Banach space. Using this result, we prove a fixed point theorem for nonexpansive mappings in a Hilbert space and an existence theorem for maximal monotone operators in a Banach space. Received: 3 July 2006 Revised: 15 January 2007     

Characterizations of reproducing cones and uniqueness of fixed points

The purpose of this paper is to discuss the existence and uniqueness of fixed point in a partially ordered Banach space. Based on the characterizations of reproducing cones, some fixed point theorems for nonlinear operators are proved. As an application, the existence and uniqueness of periodical solution for a first order differential equation is discussed.     

几类非紧减算子的新的不动点定理及其应用

研究了在四种不同条件下非紧减算子的不动点的存在性,得到了几个新的不动点定理,最后给出了一个应用的例子.     

一类凹与凸算子的推广

运用锥的性质以及单调迭代技巧给出了一类广义凹算子与凸算子正不动点的存在唯一性,并讨论了算子特征值方程的性质.作为应用,利用所获结果研究了一类积分方程正解的存在唯一性.     

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.     

一类反向混合单调算子新不动点定理的推广

利用锥理论和非对称迭代方法,讨论了一类反向混合单调算子的不动点的存在唯一性,得到了若干不具有连续性和紧性条件的有关反向混合单调算子的新不动点定理,所得结果是某些已有结果的本质改进和推广.     

[[alpha]]凹算子与[[beta]]凸算子之和的多重不动点及其应用

研究存在两个正不动点的一类算子,以α(0＜α＜1)凹算子与β(β＞1)凸算子之和为特殊情形,最后把结果用于超线性二阶奇异微分方程边值问题．