下解

通过Galerkin方法、勒贝格控制收敛定理、Gronwall不等式及广义上下解方法给出一类非线性抛物&常微弱耦合方程组混合问题广义解的单调迭代法；

Galerkin method , Lebesque control-convergent theorem , Gronwall inequality and the method of generalized upper and lower solution were employed to demonstrate the monotone iteration method generalized solution for the mixed boundary value problem of the weakly coupled parabolic and ordinary system .

我们将利用正则化方法和上下解技巧给出局部古典解和整体古典解的存在唯一性。

We will use regular-ization method and upper and lower solution technique to give the local existence , global existence and uniqueness results .

DNA双螺旋链在复制和转录的过程中要在酶的催化下解旋，这是一个高度复杂的过程，目前还无法用物理学的方法来描述。

During the replication and transcription , DNA unwinds the double helix under the control of an enzyme . It is a very complex process beyond a physical description .

一类竞争扩散方程组在Neumann边条件下解的渐近行为

Asymptotic Behavior of the Solution for Neumann Boundary Condition of Competition-Diffusion System

研究Banach空间中一阶周期边值微分方程解的存在性。对适合混合单调过程的一类函数，利用上下解的混合单调方法证明了解的存在性，推广了已有的结果[4]。

An existence theorem of first order periodic boundery value problems in Banach space is proved by using the methods of mixed monotone .

本文利用上下解方法讨论了n阶非线性常微分方程的边值问题，论述了其具有两点及三点非线性边界条件的边值问题解的存在性。

Using the method of upper and lower solution this paper discusses the existence of solution of two and three point boundary value problems with nonlinear boundary conditions for nth & order nonlinear ordinary differential equation .

在自由边界条件下解出了钙钛矿结构有限尺寸晶体的简谐振动方程，发现许多简谐振子软模.用这些软模说明了钛酸钡晶体冷却时发生具有a畴和c畴结构的铁电相变。

The soft modes in a finite perovskite with free boundary were calculated , and they can be used to explain why that barium titanate crystal has a and c domain structures in ferroelectric phase transition while temperature reduces .

一类广义Sine-Gordon方程概周期解的上下解证法

Almost Periodic Solutions to Generalized Sine-Gordon Equations with Method of Upper and Lower Solutions

研究了具时滞和扩散的SIR传染病模型，利用上下解及其迭代序列方法探讨在有界区域的半线性耦合抛物型方程组的渐近行为。

A SIR epidemic model with time delay and diffusion is investigated . The dynamics of a coupled system of semilinear parabolic equations are investigated using the method of upper and lower solutions and its associated iterations .

讨论了一类广义Boussinesq系统在受控初值条件下解的渐近稳定性，分析了该Boussinesq波的渐近性态。

The asymptotic stability of controlled initial values for a generalized Boussinesq equation is given . The asymptotic behavior of this Boussinesq wave is analyzed .

用以论证的主要工具是Schauder不动点定理和上下解方法。

The main tools to prove our theorems are the sub supersolution method and the Schauder fixed point theorem .

采用bootstrap技巧，研究了带非局部边值条件的时滞的Logistic方程的正周期解的存在性和一般时变解的渐近性态的上、下解方法。

By the bootstrap , we study the upper and lower solutions mothed of the existence of positive periodic solutions and asymptotic behavior of general time-dependent solutions for Logistic equation with time delay with nonlocal boundary value conditions .

利用上下解原理的方法，研究一类生态学中的反应扩散系统VolterraLotka模型的稳定共生态。

Using the method of upper and lower solutions principle , the coexistence steady states of a kind of reaction diffusion system in ecology , the Volterra Lotka model is studied .

建立了无限区间上的积一微分方程的比较定理，用上下解方法证明了无限区间上的Banach空间积-微分方程的初值问题的解的存在性。

We establish the comparison theorem of integro & differential equations on infinite interval , and , by applying the lower-upper solution method , prove the existence of extreme solutions for nonlinear first order integro-differential equations on infinite interval in Banach spaces .

本文利用上、下解方法研究一类奇摄动非线性Volterra型积分方程的解的存在性和形式解的一致有效性。

In this paper , by means of the method of supper and lower solutions we investigate the existence of solutions and uniformly validity of formal solutions for a class of singularly perturbed nonlinear integral equations of Volterra type .

用上下解方法，研究了两点、三点、四点离散边值问题解的存在性，这类边值问题包括了Neumann边值问题和周期边值问题。

In this paper , two-point , three-point and four-point discrete boundary value problems , including Neumann boundary value problems and periodic boundary value problems , were studied with a generalized method of upper and lower solutions .

本论文主要利用上下解和单调迭代法，研究了下面的带有Neumann边界条件的二阶泛函微分方程和φ-Laplace方程在上下解反序条件下，解的存在性条件。

In this paper , we show that the method of monotone iterative technique is valid to obtain two monotone sequences converges uniformly to extremal solutions of second order functional differential equation and Laplace equation with Neumann boundary value conditions .

本文利用极大值原理研究一类非线性反应扩散方程在各种边界条件下解的Blow－up问题，给出了整体解不存在的一系列定理，并得到了Blow－up时间T的上界。

This paper , by maximum principle , concerns the problem on blow up of the solutions for a class of nonlinear reaction diffusion equations with a various of boundary conditions , and obtained some nonexistence theorems of global solutions and the bounds of the " Blow up time " T.

讨论一类具有连续分布滞量的二阶非线性偏微分方程在Robin，Dirichlet边界条件下解的振动性，利用Green定理及微积分技巧，获得该类方程解振动的充分条件。

It is discussed that the oscillation of a class of second order nonlinear partial differential equations with continuous distribution delay under Robin and Dirichlet boundary value conditions . The sufficient conditions for the oscillation of solutions of the equation are obtained by using Green 's theorem and calculus techniques .

本文对一类非线性算子的障碍问题提出了几个Schwarz算法，所得迭代序列为上解序列或下解序列，它们单调收敛于问题的准确解。

In this paper , we propose several Schwarz algorithms for obstacle problems with a type of nolinear operators . Any iterative sequence generated by the algorithms is a super-solution or a lower-solution sequence , which converges monotonically to the problem .

所涉及的数学理论包括：上下解方法、比较原理、单调动力系统理论、全局分歧理论、拓扑不动点理论、Lyapunov-Schmidt过程和扰动理论等。

The tools used here include super-sub solutions method , comparison principle , monotone system theory , global bifurcation theory , fixed-point theory of topology , Lyapunov-Schmidt procedure and perturbation technique .

利用不动点定理得到了带脉冲的奇异边值问题的上解和下解方法，并且给出了带脉冲的Emden-Fowler方程奇异边值问题正解存在的充分必要条件。

We obtain the method of lower and upper solutions to the impulsive singular boundary value problems using the fixed point theorem and give necessary and suffcient condition for the existence of positive solutions to the impulsive singular boundary value problems of Emden-Fowler equations .

一个奇异三阶微分方程的上下解方法

Upper and lower solution method for a singular third-order differential equation

弱条件下解非线性方程算法的收敛性

The Convergence of Algorithm for Solving Nonlinear Equations under Weak Condition

所得结果是利用上下解方法得到。

The results are obtained by using upper and lower solutions method .

主要探讨其平衡解的稳定性以及在适当条件下解的分岔问题。

The authors discuss the stability of steady states and the bifurcation problem .

三阶拟线性全双曲方程及其上下解序列

Third order quasilinear totally hyperbolic equations and its sequence of upper and lower solutions

四阶差分方程在多点边值条件下解的存在性

Existence of Solutions for a Fourth Order Difference Equation with Multipoint Boundary Value Condition

m点边值共振问题的上下解和拓扑度

The upper and lower solutions of m-point boundary value problems at resonance and topological degree

抽象二阶周期边值问题的上、下解方法

The method of lower and upper solutions for abstract second order periodic boundary value problems