Finding a Zero of The Sum of Two Maximal Monotone Operators

In this paper, the equivalence between variational inclusions and a generalized type of Weiner–Hopf equation is established. This equivalence is then used to suggest and analyze iterative methods in order to find a zero of the sum of two maximal monotone operators. Special attention is given to the case where one of the operators is Lipschitz continuous and either is strongly monotone or satisfies the Dunn property. Moreover, when the problem has a nonempty solution set, a fixed-point procedure is proposed and its convergence is established provided that the Brézis–Crandall–Pazy condition holds true. More precisely, it is shown that this allows reaching the element of minimal norm of the solution set.     

Controllability of Impulsive Evolution Inclusions with Nonlocal Conditions

In this paper, we examine controllability problems of evolution inclusions with nonlocal conditions. Using the set-valued and single-valued Mönch fixed-point theorem, we establish some sufficient conditions for the controllability under convex and nonconvex orientor fields respectively. Our approach is different from all previous approaches; we do not assume that the evolution system generates a compact semigroup; so, our method is applicable to a wide class of (impulsive) control systems and evolution inclusions in Banach spaces.     

球面上连续映射的一些新结果

本文研究了从球面到欧氏空间连续映射的性质.利用Brouwer映射度理论和微分拓扑的基本方法,获得了Borsuk-Ulam型定理,推广了Borsuk-Ulam定理.     

Qualitative analysis of 3D elastostatic contact problems with orthotropic Coulomb friction and solution-dependent coefficients of friction

This paper analyzes a discrete form of 3D contact problems with local orthotropic Coulomb friction and coefficients of friction which may depend on the solution itself. The analysis is based on the fixed-point reformulation of the original problem. Conditions guaranteeing the existence and uniqueness of discrete solutions are established. Finally, numerical results of a model example are presented.     

Solutions to Boundary Value Problem of Nonlinear Impulsive Differential Equation of Fractional Order

This paper is devoted to study the existence and uniqueness of solutions to a boundary value problem of nonlinear fractional differential equation with impulsive effects.The arguments are based upon Schauder and Banach fixed-point theorems. We improve and generalize the results presented in[B.Ahmad,S.Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations,Nonlinear Analysis：Hybrid Systems,3（2009）,251- 258].     

An Application of Darbo Fixed-Point Theorem to a Class of Functional Integral Equations

In this article, using Darbo's fixed-point theorem associated with the measure of noncompactness, we prove a theorem on the existence of the solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. Our existence results include several existence results obtained earlier by Maleknejad et al. [7 K. Maleknejad , K. Nouri , and R. Mollapourasl ( 2009 ). Investigation on the existence of solutions for some nonlinear functional-integral equations . Nonlinear Anal. 71 : 1575 – 1578 .[Crossref], [Web of Science ®] , [Google Scholar]] and Özdemir et al. [8 ?. Özdemir , Ü. Çakan , and B. ?lhan ( 2013 ). On the existence of the solutions for some nonlinear Volterra integral equations . Abstr. Appl. Anal. Article ID 689234.  [Google Scholar]] as special cases under some weaker conditions. We give also some examples which show that our results are applicable.     

Positive solutions to m-point boundary value problem of fractional differential equation

In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations: Dqu(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) =sum (μiDpu(t)|t = ξi ) from i =1 to ∞ m-2, where q ∈R , 1 相似文献   

Attractive fixed-point solution study of shell model for homogeneous isotropic turbulence

The attractive fixed-point solution of a nonlinear cascade model is studied for the homogeneous isotropic turbulence containing a parameter C, introduced by Desnyansky and Novikov. With a traditional constant positive external force added on the first shell equation, it can be found that the attractive fixed-point solution of the model depends on both the parameter C and the external force. Thus, an explicit force is introduced to remove the effects of the external force on the attractive fixed-point solution. Furthermore, two groups of attractive fixed-point solutions are derived theoretically and studied numerically. One of the groups has the same scaling behavior of the velocity in the whole inertial range and agrees well with those observed by Bell and Nelkin for the nonnegative parameters. The other is found to have different scaling behaviors of the velocity at the odd and even number shells for the negative parameters. This special characteristic may be used to study the anomalous scaling behavior of the turbulence.