二阶非线性微分方程的单调解

本文讨论了一类二阶非线性常微分方程的单调解，给出了方程存在Ｂ类解的充要条件，部分地回答了Ｍａｒｉｎｉ在ＮｏｎｌｉｎｅａｒＡｎａｌｙｓｉｓ上提出的两个问题．

关于方程x^((n))+px=0的单调解和振动解

自从1836年Sturm就二阶浅性方程x"+Qx=0发表著名的0点“分离定理”和“比较定理”以来,关于形如xn+px=0方程的解的性态,一直是人们感兴趣的课题,1977年W.J.Klm假定当t→∞时,有x≥0和x/t2→0或x/t→0,在这种假设下,讨论了方程的单调解和振动解。

一类中立型偏差分方程单调解的不存在性

采用分析的方法考虑了一类具有变系数的非线性中立型时滞偏差分方程的单调解的不存在性.得到了该方程不存在单调解的几个充分条件,并改进了以前的一个结果.

二阶非线性微分方程单调解的性质

二阶非线性微分方程解的特性研究很重要。Ｍａｒｉｎｉ．Ｍ对一类二阶非线性微分方程在一定条件下解的单调性质提出一个问题，作者列举正反两例说明此问题的结论是不确定的．

二阶非线性时滞微分方程的单调解(英文)

运用黎卡提变换研究了一类非线性时滞微分方程 ,得到了它的单调解存在性的充要条件 ,并应用这些条件获得了这类方程单调解存在性的几个判据与比较定理 .

非齐次边界条件下两点边值问题单调解的存在性

研究了一类二阶非线性微分方程在非齐次边界条件下的两点边值问题单调解的存在性.运用锥拉伸与锥压缩不动点定理,分别得到了边值问题单调递增正解和单调递减负解存在的充分条件.

某些三阶三点边值问题的可解性

本文考虑如下三阶三点边值问题：ｘ＝ｆ（ｔ，ｘ，ｘ′，ｘ″）（０≤ｘ≤１），ｘ∈Ｂ，其中Ｂ表以下边值条件之一：ｘ′（０）＝ｘ′（１）＝ｘ（ξ）＝０，ｘ′（０）＝ｘ″（１）＝ｘ（ξ）＝０，ｘ″（０）＝ｘ′（１）＝ｘ（ξ）＝０，ξ∈［０，１］是给定的．对以上边值问题，给出不限制ｆ增长的可解条件．

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.

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.

Periodic Boundary Value Problem for Functional Differential Equations with Impulses

Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.

Periodic Solutions of Periodic Delay Predator-Prey System with Nonmonotonic Functional Response

By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional response in a periodic environment.

Global Existence in H^2 for a 1-d Non-monotone Fluid

In this paper, we prove the existence in H＋^2, an incomplete metric subspace of H^2×H^2×H^2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=（0,1）. The results in this paper have improved those previously related results.

Coexistence of a Strongly Coupled Prey-predator Model for Holling's Type Ⅲ

In this paper, the two-species prey-predator Lotka-Volterra model with the Holling＇s type III is discussed. By the method of coupled upper and lower solutions and its associated monotone iterations, the existence of solutions for a strongly coupled elliptic system with homogeneous of Dirchlet boundary conditions is derived. These results show that this model admits at least one coexistence state if across-diffusions are weak.

Monotone Iterative Technique for Duffie-Epstein Type Backward Stochastic Differential Equations

For Duffle-Epstein type Backward Stochastic Differential Equations, the comparison theorem is proved. Based on the comparison theorem, by monotone iterative technique, the existence of the minimal and maximal solutions of the equations are proved.

A Nonmonotone Trust Region Method for Solving Symmetric Nonlinear Equations

A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems.

Implicit Variational Inclusions and Algorithms Involving （A, η）-monotone Operators in 2-uniformly Smooth Banach Spaces

This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving （A, η）-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the （A, η）-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving （H, η）-monotone mappings.

一类含一阶导数项两点边值问题单调正解的存在性

研究一类含有一阶导数项的二阶微分方程在非齐次边界条件下的两点边值问题单调解的存在性.利用锥拉伸与锥压缩不动点定理,给出了边值问题单调递增正解和单调递减负解存在的充分条件,并且对解的凸性进行了分析.

Magnetic Properties of One-Dimensional Ferromagnetic Mixed-Spin Model within Tyablikov Decoupling Approximation

In this paper, we apply the two-time Green's function method, and provide a simple way to study themagnetic properties of one-dimensional spin-(S, s) Heisenberg ferromagnets.The magnetic susceptibility and correlationfunctions are obtained by using the Tyablikov decoupling approximation.Our results show that the magnetic susceptibilityand correlation length are a monotonically decreasing function of temperature regardless of the mixed spins.It isfound that in the case of S = s, our results of one-dimensional mixed-spin model is reduced to be those of the isotropicferromagnetic Heisenberg chain in the whole temperature region.Our results for the susceptibility are in agreement withthose obtained by other theoretical approaches.

Regularization Semismooth Newton Method for P_0-NCPs with Non-monotone Line Search

Based on the generalized Fischer-Burmeister function, Chen et al in 2008 put forward a regularization semismooth Newton method for solving the nonlinear complementarity problem with a P0-function. In this paper, we investigate the above algorithm with the monotone line search replaced by a non-monotone line search. It is shown that the non-monotone algorithm is well-defined, and is globally and locally superlinearly convergent under standard assumptions.

Note on Some Oscillation Theorems in a Recent Paper

In this paper, some counterexamples are offered to illustrate that some results stated in a recent paper on the oscillatory behavior of solutions of second order nonlinear difference equation are incorrect.