一类具p-Laplacian算子的多点边值问题单调迭代正解的存在性

利用单调迭代的方法得到了一类具p-Laplacian算子的多点边值问题单调迭代正解的存在性,同时也得到了解的相应迭代序列.     

一类2n阶次线性奇异边值问题的正解

利用单调迭代方法给出了一类2n阶次线性奇异常微分方程正解的存在性,得到C~(2n-2)[0,1]和C~(2n-1)[0,1]正解存在的充分必要条件,也得到正解的唯一性.     

半直线上具有p-Laplacian算子的Sturm-Liouville型脉冲边值问题的单调迭代正解

利用单调迭代方法得到了半直线上具有p-Laplacian算子的脉冲微分方程边值问题单调迭代正解的存在性,同时也给出了解的相应迭代序列.     

无穷区间上具有p-Laplacian算子的脉冲多点边值问题单调迭代正解的存在性

利用单调迭代方法得到了无穷区间上具有p-Laplacian算子的脉冲微分方程多点边值问题单调迭代正解的存在性,同时也给出了解的相应迭代序列.     

半直线上Riemann-Liouville型奇异分数阶微分方程边值问题的单调迭代方法

运用不动点定理和单调迭代方法研究半直线上Riemann-Liouville型奇异分数阶微分方程边值问题的正解的存在性.在没有上、下解存在的假设下建立了边值问题存在两个正解的结果,构造了逼近正解的迭代格式,该迭代格式便于应用.     

带变号系数的经典Gelfand模型的正解

考察了经典Gelfand模型的正解的存在与迭代,其中非线性项的系数允许在[0,1]中改变符号。利用单调迭代方法得到了一个正解存在定理,给出了相应的迭代程序和收敛速度。由于这个迭代程序是从零函数开始的,因此它是简单、可行并且有效的。     

二阶非线性q-差分微分方程两点边值问题两个迭代正解的存在性*

研究了二阶非线性q-差分微分方程两点边值问题,给出了系统两个正解存在的充分条件. 与其他文献中使用的不动点定理不同,文章不仅证明了该系统正解的存在性, 而且还利用单调迭代技巧给出了逼近正解的迭代格式.     

2n阶Lidstone边值问题正解的逐次迭代

研究了2n阶Lidstone边值问题正解的逐次迭代,其中非线性项依赖于所有偶数阶导数.通过考察非线性项在某些有国介集合上的“高度”并利用单调迭代方法构造了一个逐次迭代程序.这个迭代程序从一个多项式开始并且是可行的.使用这个结论获得了m个正解的迭代方法,其中m是一个任意的自然数.     

一类阿达马分数阶微分方程在无穷区间上的的正解（英文）

利用Banach压缩映像原理以及构造一个显式迭代,得到阿达马分数阶微分方程在无穷区间上的正解的存在唯一性结果.而且,我们给出了一个误差估计.     

Banach空间中二阶非线性奇异微分方程多点无穷边值问题的正解

利用锥理论和Mōnch不动点定理结合单调迭代技巧,研究了Banach空间中一类二阶非线性奇异微分方程多点无穷边值问题,获得了正解的存在性定理和正解的迭代序列.     

Scalarization and optimality conditions for vector equilibrium problems

In this paper, we investigated vector equilibrium problems and gave the scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provided the necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we gave sufficient conditions for those solutions. As applications, we gave the necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems.     

Rational Solutions to the KdV Equation in Terms of Particular Polynomials

Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order $n$ for any positive integer $n$, and we call these solutions, solutions of the order $n$. Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order $10$.     

On the convective Cahn-Hilliard equation with degenerate mobility

In this paper, we study the existence of weak solutions for the convective Cahn-Hilliard equation with degenerate mobility. Based on the Schauder type estimates, we establish the global existence of classical solutions for regularized problems. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.     

Forward dynamic utility functions: A new model and new results

A major obstacle in the existing models of forward dynamic utilities and investment performance evaluation is to establish the existence and uniqueness of the optimal solutions. Consequently, we present a new model of forward dynamic utilities. In doing so, we establish the existence and uniqueness of the solutions for a general (smooth) utility function, and we show that the assumptions needed for such solutions are similar to those under the backward formulation. Moreover, we provide unique viscosity solutions. We also provide discontinuous viscosity solutions. In addition, we introduce Hausdorff-continuous viscosity solutions to the portfolio model.     

Blow-up Dynamics of L~2 Solutions for the Davey–Stewartson System

We study the blow-up solutions for the Davey–Stewartson system(D–S system, for short)in L2x(R2). First, we give the nonlinear profile decomposition of solutions for the D–S system. Then, we prove the existence of minimal mass blow-up solutions. Finally, by using the characteristic of minimal mass blow-up solutions, we obtain the limiting profile and a precisely mass concentration of L2 blow-up solutions for the D–S system.     

Picard and Chazy solutions to the Painlevé VI equation

We study the solutions of a particular family of Painlevé VI equations with parameters and , for . We show that in the case of half-integer , all solutions can be written in terms of known functions and they are of two types: a two-parameter family of solutions found by Picard and a new one-parameter family of classical solutions which we call Chazy solutions. We give explicit formulae for them and completely determine their asymptotic behaviour near the singular points and their nonlinear monodromy. We study the structure of analytic continuation of the solutions to the PVI equation for any such that . As an application, we classify all the algebraic solutions. For half-integer, we show that they are in one to one correspondence with regular polygons or star-polygons in the plane. For integer, we show that all algebraic solutions belong to a one-parameter family of rational solutions. Received: 23 February 1999 / Accepted: 10 January 2001 / Published online: 18 June 2001     

二阶泛函微分方程的振动性质

在本文中，我们研究了一类较广泛的二阶非线性泛函微分方程的振动性质。文中指出，在一定条件下，方程的非振动解仅有两类，而且给出了每一类非振动解存在的必要条件，同时也建立了方程振动的若干充分判据。     

A systematic method for solving differential-difference equations

A systematic method for searching travelling-wave solutions to differential-difference equations (DDEs) is proposed in the paper. First of all, we introduce Bäcklund transformations for the standard Riccati equation which generate new exact solutions by using its simple and known solutions. Then we introduce a kind of formal polynomial solutions to DDEs and further determine the explicit forms by applying the balance principle. Finally, we work out exact solutions of the DDEs via substituting the form solutions and solving over-determined algebraic equations with the help of Maple. As illustrative examples, we obtain the travelling-wave solutions of the (2 + 1)-dimensional Toda lattice equation, the discrete modified KdV (mKdV) equation, respectively.     

Solutions to the system of operator equations AXB=C=BXA

In this paper, we present some necessary and sufficient conditions for the existence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB=C=BXA in the setting of bounded linear operators on a Hilbert space. Moreover, we obtain the general forms of solutions, hermitian solutions and positive solutions to the system above.     

Global solutions and self‐similar solutions for coupled nonlinear Schrödinger equations

In this paper, we prove the existence and uniqueness for the global solutions of Cauchy problem for coupled nonlinear Schrödinger equations and obtain the continuous dependence result on the initial data and the stronger decay estimate of global solutions. In particular, we show the existence and uniqueness of self‐similar solutions. Also, we build some asymptotically self‐similar solutions. Copyright © 2017 John Wiley & Sons, Ltd.