Planar competitive and cooperative difference equations

This paper focuses on the asymptotic behavior of planner order-preserving difference equations with particular attention to those arising from models of two-species competition.     

Coupled fixed point results for nonlinear integral equations

In this paper, we prove some coupled coincidence point theorems for such nonlinear contraction mappings having a mixed monotone property in partially ordered metric spaces by dropping the condition of commutative. We also prove coupled common fixed point theorem for w-compatible mappings. An example of a nonlinear contraction mapping which is not applied by Lakshmikantham and ?iri?’s theorem [1] but applied by our result is given. Further, we apply our results to the existence theorem for solution of nonlinear integral equations.     

一个积分不等式

由连续单调函数的几何意义直观地得出一个不等式,即若设函数f（x）在[0,b]上连续且单调递减,则有b∫0^af（x）dx≥a∫0^bf（x）dx（0≤a≤b）.通过构造辅助函数给出其数学证明,并对其加以推广．     

A class of discrete time generalized Riccati equations

In this paper, a class of discrete-time backward non-linear equations defined on some ordered Hilbert spaces of symmetric matrices is considered. The problem of the existence of some global solutions is investigated. The class of considered discrete-time non-linear equations contains, as special cases, a great number of difference Riccati equations both from the deterministic and the stochastic framework. The results proved in the paper provide the sets of necessary and sufficient conditions that guarantee the existence of some special solutions of the considered equations as: the maximal solution, the stabilizing solution and the minimal positive semi-definite solution. These conditions are expressed in terms of the feasibility of some suitable systems of linear matrix inequalities (LMI). One shows that in the case of the equations with periodic coefficients to verify the conditions that guarantee the existence of the maximal or the stabilizing solution, we have to check the solvability of some systems of LMI with a finite number of inequations. The proofs are based on some suitable properties of discrete-time linear equations defined by the positive operators on some ordered Hilbert spaces chosen adequately. The results derived in this paper provide useful conditions that guarantee the existence of the maximal solution or the stabilizing solution for different classes of difference matrix Riccati equations involved in many problems of robust control both in the deterministic and the stochastic framework. The proofs are deterministic and are accessible to the readers less familiarized with the stochastic reasonings.     

A note on the dependence on parameters for a nonlinear system via monotonicity theory

Using monotonicity theory, we investigate the continuous dependence on parameters for the discrete BVPs, which can be written in a form of a nonlinear system.     

Global existence result for thermoviscoelastic problems with hysteresis

We consider viscoelastic solids undergoing thermal expansion and exhibiting hysteresis effects due to plasticity or phase transformations. Within the framework of generalized standard solids, the problem is described in a three-dimensional setting by the momentum equilibrium equation, the flow rule describing the dependence of the stress on the strain history, and the heat transfer equation. Under appropriate regularity assumptions on the data, a local existence result for this thermodynamically consistent system is established, by combining existence results for ordinary differential equations in Banach spaces with a fixed-point argument. Then global estimates are obtained by using both the classical energy estimate and more specific techniques for the heat equation introduced by Boccardo and Gallouët. Finally a global existence result is derived.     

L-凸空间中一个新的连续选择及其不动点定理以及对抽象经济的应用(英文)

在L-凸空间中建立了一个新的连续选择及其不动点定理.作为应用,获得了L-凸空间中的极大元定理以及定性对策和抽象经济的平衡点存在定理     

一类带Stenfen-Boltzmann 边界条件的热输运反问题的单调算法

在钢体铸造过程中, 当钢铁在钢包中被加热并且融化后, 如何探测接近高温铁水的钢包内壁是否出现了腐蚀现象是一个重要的问题. 我们尝试通过钢包外表面的温度知道内部腐蚀的情况. 本文得到了表面温度关于内部腐蚀区域的“拟单调” 性质, 并由此提出解决边界反演问题的数值算法. 数值例子表明本文算法是有效的.     

Local Hardy spaces of Musielak-Orlicz type and their applications

Letφ:R n × [0,∞) → [0,∞) be a function such that φ(x,·) is an Orlicz function and (·,t) ∈ A ∞loc (Rn) (the class of local weights introduced by Rychkov).In this paper,the authors introduce a local Musielak-Orlicz Hardy space hφ(Rn) by the local grand maximal function,and a local BMO-type space bmoφ(Rn) which is further proved to be the dual space of hφ(Rn).As an application,the authors prove that the class of pointwise multipliers for the local BMO-type space bmo φ (Rn),characterized by Nakai and Yabuta,is just the dual of L 1 (Rn) + h Φ 0 (Rn),where φ is an increasing function on (0,∞) satisfying some additional growth conditions and Φ 0 a Musielak-Orlicz function induced by φ.Characterizations of hφ(Rn),including the atoms,the local vertical and the local nontangential maximal functions,are presented.Using the atomic characterization,the authors prove the existence of finite atomic decompositions achieving the norm in some dense subspaces of hφ(Rn),from which,the authors further deduce some criterions for the boundedness on hφ(Rn) of some sublinear operators.Finally,the authors show that the local Riesz transforms and some pseudo-differential operators are bounded on hφ(Rn).     

Proofs with monotone cuts

Atserias, Galesi, and Pudlák have shown that the monotone sequent calculus MLK quasipolynomially simulates proofs of monotone sequents in the full sequent calculus LK (or equivalently, in Frege systems). We generalize the simulation to the fragment MCLK of LK which can prove arbitrary sequents, but restricts cut‐formulas to be monotone. We also show that MLK as a refutation system for CNFs quasipolynomially simulates LK.