三维空间中半线性波动方程组的整体解和自相似解

本文证明了一类半线性波动方程组Cauchy问题整体解的存在唯一性．特别地,证明了自相似解的存在唯一性．同时还得到了渐近自相似解．     

Existence and uniqueness of solutions of piecewise nonlinear systems

In this paper, we consider the existence and the uniqueness of solutions of piecewise nonlinear systems. We will present some necessary and sufficient conditions for the existence and the uniqueness of solutions of this class of systems.     

Existence and uniqueness of solutions of piecewise nonlinear systems

In this paper, we consider the existence and the uniqueness of solutions of piecewise nonlinear systems. We will present some necessary and sufficient conditions for the existence and the uniqueness of solutions of this class of systems.     

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.     

二阶常微分方程及Thomas－Fermi方程的边值问题

本文利用上、下解方法推广了Ｍ．Ｌｅｅｓ关于半线性边值问题的结果，给出了另一类边值问题解的存在唯一性的一个充分条件；并利用所得的结果证明了Ｔｈｏｍａｓ－Ｆｅｒｍｉ方程的边值问题解的存在唯一性，从而推广了Ｃ．ＤＬｕｎｉｎｇ的结果．     

Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients

In this paper we extend recent results on the existence and uniqueness of solutions of ODEs with non-smooth vector fields to the case of martingale solutions, in the Stroock-Varadhan sense, of SDEs with non-smooth coefficients. In the first part we develop a general theory, which roughly speaking allows to deduce existence, uniqueness and stability of martingale solutions for Ld-almost every initial condition x whenever existence and uniqueness is known at the PDE level in the L^∞-setting (and, conversely, if existence and uniqueness of martingale solutions is known for Ld-a.e. initial condition, then existence and uniqueness for the PDE holds). In the second part of the paper we consider situations where, on the one hand, no pointwise uniqueness result for the martingale problem is known and, on the other hand, well-posedness for the Fokker-Planck equation can be proved. Thus, the theory developed in the first part of the paper is applicable. In particular, we will study the Fokker-Planck equation in two somehow extreme situations: in the first one, assuming uniform ellipticity of the diffusion coefficients and Lipschitz regularity in time, we are able to prove existence and uniqueness in the L²-setting; in the second one we consider an additive noise and, assuming the drift b to have BV regularity and allowing the diffusion matrix a to be degenerate (also identically 0), we prove existence and uniqueness in the L^∞-setting. Therefore, in these two situations, our theory yields existence, uniqueness and stability results for martingale solutions.     

Existence and Uniqueness of Solutions for Time-Fractional Oldroyd-B Fluid Equations with Generalized Fractional Derivatives

In this paper, we study the existence and uniqueness of solutions for time-fractional Oldroyd-B fluid equations with generalized fractional derivatives. We distinguish two cases. Firstly for the linear case, we get regularity results under some hypotheses of the source function and the initial data. Secondly for the nonlinear case, we use the Banach fixed point theorem to obtain the existence and uniqueness of solutions.     

一个非局部方程解的存在性

本文旨在讨论一个线性非局部方程和相应非线性方程解存在的条件，对非局部积分核作一定限制后，得到在积分核变号条件下解的存在唯一性结果。     

二阶常系数中立型方程的周期解

讨论了一类二阶常系数中立型方程的周期解的存在性与唯一性，获得了保证周期解存在唯一的具体条件。     

n阶非线性常微分方程的非线性两点边值问题

本文利用打靶法,给出了ｎ阶非线性常微分方程具有非线性两点边界条件的边值问题存在解与存在唯一解的一般性结果,并将所得结果应用于Ｌｉｐｓｃｈｉｔｚ方程的两点过值问题,给出了存在解与存在唯一解的具体的充分条件。     

Existence and uniqueness of solutions for third-order nonlinear boundary value problems

In this paper, we present some general results of existence and uniqueness of solutions of nonlinear two-point boundary value problems for third-order nonlinear differential equations by using the Shooting method. As applications we give certain concrete sufficient conditions for the existence and uniqueness.     

Entropy and renormalized solutions to the general nonlinear elliptic equations in Musielak–Orlicz spaces

In this paper we mainly prove the existence and uniqueness of entropy solutions and the uniqueness of renormalized solutions to the general nonlinear elliptic equations in Musielak-Orlicz spaces. Moreover, we also obtain the equivalence of entropy solutions and renormalized solutions in the present conditions.     

一类混合似变分不等式问题解的存在唯一性

本文中,我们首先给出了一类混合似变分不等式问题．接着,在Banach空间中研究了它的解的存在性和唯一性．最后,讨论了混合似变分不等式问题的扰动问题,并证明了扰动问题的解的存在唯一性定理．     

PERIODIC SOLUTIONS TO A HIGH-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,using the principle of a priori boundedness,we study the existence and uniqueness of periodic solutions to a high-order neutral functional differential equation.Some new results for the existence and uniqueness of the periodic solution are obtained.     

一类退化抛物方程的边值问题

In this paper, we study the boundary value problem (BVP) for a degenerate parabolic equation. By introducing a proper notion of weak solutions, we prove the uniqueness and existence of weak solutions of the problem. The localization of weak solutions is also discussed, which plays a key role in the proof of the uniqueness.     

中立型脉冲发展方程解的存在性和唯一性

本文研究了一类非线性中立型脉冲发展方程解的存在性和唯一性的问题.利用迭代分析方法结合半群理论的知识,得到了其解的表达式,并构造解的迭代序列,同时证明了其解的存在性和唯一性.通过研究发现其解的存在性和唯一性与脉冲时滞条件密不可分,利用迭代分析法求解此类问题具有一定的优越性.     

Some results on a singular parabolic equation in one dimension case

This paper is concerned with the existence, nonexistence, uniqueness, and non‐uniqueness of solutions for a singular parabolic equation in one dimension case. For different cases of some constant m of the equation, we study the uniqueness of solutions for m > ? 1, the nonexistence of solutions for m ≤ ? p, and the existence and non‐uniqueness of solutions for ? p < m ≤ ? 1. The novelty of this paper lies in the study of nonexistence. Moreover, the other results of this paper extend some recent works. Copyright © 2013 John Wiley & Sons, Ltd.     

四阶非线性周期系统周期解的存在唯一性

本文利用Liapunov函数方法,研究了一类具有缓变系数的四阶非线性非自治周期系统的周期解的存在唯一性及其渐近稳定性.我们得到了保证这些系统存在唯一稳定周期解的充分条件,并对系数的缓变范围作了较为精确的估计.     

Existence of positive solutions of nonlinear fractional delay differential equations

This paper investigates the existence and uniqueness of positive solutions for a class of nonlinear fractional delay differential equations. Using a nonlinear alternative of Leray-Schauder type, we show the existence of positive solutions for the equations in question.     

Uniqueness of traveling wave solutions for a biological reaction-diffusion equation

The existence of traveling wave solutions for a reaction-diffusion, which serves as models for microbial growth in a flow reactor and for mathematical epidemiology, was previously confirmed. However, the problem on the uniqueness of traveling wave solutions remains open. In this paper we give a complete proof of the uniqueness of traveling wave solutions.